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## Walking Paths to and from a Goal Differ: On the Role of Bearing Angle in the Formation of Human Locomotion Paths

Fonte: Public Library of Science
Publicador: Public Library of Science

Tipo: Artigo de Revista Científica

Publicado em 10/04/2015
EN

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The path that humans take while walking to a goal is the result of a cognitive process modulated by the perception of the environment and physiological constraints. The path shape and timing implicitly embeds aspects of the architecture behind this process. Here, locomotion paths were investigated during a simple task of walking to and from a goal, by looking at the evolution of the position of the human on a horizontal (x,y) plane. We found that the path while walking to a goal was not the same as that while returning from it. Forward-return paths were systematically separated by 0.5-1.9m, or about 5% of the goal distance. We show that this path separation occurs as a consequence of anticipating the desired body orientation at the goal while keeping the target in view. The magnitude of this separation was strongly influenced by the bearing angle (difference between body orientation and angle to goal) and the final orientation imposed at the goal. This phenomenon highlights the impact of a trade-off between a directional perceptual apparatus—eyes in the head on the shoulders—and and physiological limitations, in the formation of human locomotion paths. Our results give an insight into the influence of environmental and perceptual variables on human locomotion and provide a basis for further mathematical study of these mechanisms.

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## Calculation of Blocking Probabilities in Multistage Interconnection Networks with Redundant Paths

Fonte: MIT - Massachusetts Institute of Technology
Publicador: MIT - Massachusetts Institute of Technology

Formato: 1073151 bytes; 836222 bytes; application/postscript; application/pdf

EN_US

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The blocking probability of a network is a common measure of its performance. There exist means of quickly calculating the blocking probabilities of Banyan networks; however, because Banyan networks have no redundant paths, they are not inherently fault-tolerant, and so their use in large-scale multiprocessors is problematic. Unfortunately, the addition of multiple paths between message sources and sinks in a network complicates the calculation of blocking probabilities. A methodology for exact calculation of blocking probabilities for small networks with redundant paths is presented here, with some discussion of its potential use in approximating blocking probabilities for large networks with redundant paths.

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## Time-optimal CNC tool paths : a mathematical model of machining; Time-optimal Computer Numerical Control tool paths : a mathematical model of machining

Fonte: Massachusetts Institute of Technology
Publicador: Massachusetts Institute of Technology

Tipo: Tese de Doutorado
Formato: 188 p.; 15692109 bytes; 15691866 bytes; application/pdf; application/pdf

ENG

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Free-form surface machining is a fundamental but time-consuming process in modern manufacturing. The central question we ask in this thesis is how to reduce the time that it takes for a 5-axis CNC (Computer Numerical Control) milling machine to sweep an entire free-form surface in its finishing stage. We formulate a non-classical variational time-optimization problem defined on a 2-dimensional manifold subject to both equality and inequality constraints. The machining time is the cost functional in this optimization problem. We seek for a preferable vector field on a surface to obtain skeletal information on the toolpaths. This framework is more amenable to the techniques of continuum mechanics and differential geometry rather than to path generation and conventional CAD/CAM (Computer Aided Design and Manufacturing) theory. After the formulation, this thesis derives the necessary conditions for optimality. We decompose the problem into a series of optimization problems defined on 1-dimensional streamlines of the vector field and, as a result, simplify the problem significantly. The anisotropy in kinematic performance has a practical importance in high-speed machining. The greedy scheme, which this thesis implements for a parallel hexapod machine tool...

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## Orthopyroxene-sillimanite-quartz assemblages: distribution, petrology, quantitative P-T-X constraints and P-T paths

Fonte: Blackwell Publishing Ltd
Publicador: Blackwell Publishing Ltd

Tipo: Artigo de Revista Científica

Publicado em //2003
EN

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Granulite facies magnesian metapelites commonly preserve a wide array of mineral assemblages and reaction textures that are useful for deciphering the metamorphic evolution of a terrane. Quantitative pressure, temperature and bulk composition constraints on the development and preservation of characteristic peak granulite facies mineral assemblages such as orthopyroxene + sillimanite + quartz are assessed with reference to calculated phase diagrams. In NCKFMASH and its chemical subsystems, peak assemblages form mainly in high-variance fields, and most mineral assemblage changes reflect multivariant equilibria. The rarity of orthopyroxene–sillimanite–quartz-bearing assemblages in granulite facies rocks reflects the need for bulk rock XMg of greater than approximately 0.60–0.65, with pressures and temperatures exceeding c. 8 kbar and 850 °C, respectively. Cordierite coronas mantling peak minerals such as orthopyroxene, sillimanite and quartz have historically been used to infer isothermal decompression P–T paths in ultrahigh-temperature granulite facies terranes. However, a potentially wide range of P–T paths from a given peak metamorphic condition facilitate retrograde cordierite growth after orthopyroxene + sillimanite + quartz...

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## Spatial and temporal variability of Cross-Basin acoustic ray paths

Fonte: Monterey, California: Naval Postgraduate School
Publicador: Monterey, California: Naval Postgraduate School

Tipo: Tese de Doutorado

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Approved for public release; distribution is unlimited.; It was suggested by Munk and Forbes (1989) that climate induced changes in ocean temperature may be monitored by measurements of cross-basin acoustic travel time variability. The feasibility of such a monitoring system depends on the spatial and temporal variability of the cross-basin acoustic paths in the presence of ocean variability of many different scales. For this thesis the variations in arrival position, azimuthal arrival angle, ray trajectory and the corresponding changes in travel times along the three- dimensional multipaths due to meso- and gyre scale ocean temperature fluctuations were analyzed. Emphasis was placed on the acoustic paths from Heard Island in the Indian Ocean, the proposed location for the sound source, to the west coast of the United States. An optimal receiver site location was found to exist in the vicinity of Monterey Bay, California. The possibility of a proposed listening site location near Coos Bay, Oregon, was also examined. However, the ray paths to Coos Bay interact with the bottom frequently, thus rendering them less reliable. All the ray traces for this study were carried out using the recently upgraded Hamiltonian raytracing code HARPO...

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## Trajetórias de vida : lembranças, caminhos e constituições dos saberes docentes de professores de Educação Física = Paths and trajectories of life : memories, paths and establishment of teaching knowledge of Physical Education Professors; Paths and trajectories of life : memories, paths and establishment of teaching knowledge of Physical Education Professors

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em //012
PT

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#Autobiografia#Educação física escolar#Educação física - Formação profissional#Historia de vida#Saberes docentes#Autobiography#Physical education at school#Physical education#Life history#Teaching knowledge#Narrative research (Research methods)

O objetivo da pesquisa foi traçar a trajetória biográfica percorrida por seis professores de Educação Física ao longo da vida para compreender os processos de formação docente e o itinerário de constituição de seus respectivos saberes. Para isso, a pesquisa buscou alcançar os elementos biográficos que tornaram os sujeitos professores e, em seguida, reconstruir o fluxo de constituição dos saberes. A primeira fase da pesquisa, desenvolvida a partir de um conjunto de entrevistas, deu-se com a solicitação de lembranças acerca de diferentes etapas da vida (Educação Familiar, Educação Básica, Formação Acadêmica e Experiências Profissionais). Na segunda fase os professores foram convidados a realizar análise compreensivo-reflexiva (reflexão autobiográfica) do material relatado, que objetivou a análise sobre a existência ou não de aspectos do que foi relatado que ainda influenciasse ou que já tivesse influenciado na formação e atuação profissional. Participou deste estudo um professor com três anos de docência; outro com quatro anos; outro com dezesseis anos; outro professor com vinte e um anos e dois professores com trinta anos de profissão. Os professores, ao longo do exercício de reflexão autobiográfica...

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## Uma fórmula de Itô-Ventzell para caminhos Hölder; An Itô-Ventzell type formula for Hölder paths

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 19/09/2014
PT

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#Teoria de rough path#Equações diferenciais parciais#Análise estocástica#Rough path theory#Partial differential equations#Stochastic analysis

Provaremos uma fórmula do tipo Itô-Ventzel para caminhos Hölder cujo expoente é maior que 1/3. Os exemplos fundamentais de caminhos onde a fórmula é válida é o movimento Browniano fracionário. Nossa fórmula estende (e coincide) a versão clássica feita por H. Kunita na década de 80. As ferramentas utilizadas residem no contexto dos rough paths seguindo a abordagem de M. Gubinelli. Tais tecnicas começaram a serem desenvolvidas por T. Lyons no final de 90. Como aplicação, estudaremos equações diferenciais dirigidas por caminhos cujo expoente é maior que 1/2 (Sistemas de Young). Onde a idéia aqui é empregar nossa fórmula aplicando o método das caracteristicas nesse contexto, seguindo novamente os trabalhos de H. Kunita.; We prove an Itô-Ventezel type formula for Hölder paths with exponent is greater than 1/3. The most important class of examples of theses paths is given by fractional Brownian motion. Our formula is an extension (and agree) to classic version done by H. Kunita in 80's. The technical tools used rely on rough path theory following M. Gubinelli's approach. Those techniques were developed in the late 90's. by T. Lyons. As an application, we study differential equations driven by paths with exponent greater than 1/2 (Young Systems). The ideia here is to employ our formula together with method of characteristics in this setting...

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## Longitudinal Impact of the Project PATHS on Adolescent Risk Behavior: What Happened after Five Years?

Fonte: The Scientific World Journal
Publicador: The Scientific World Journal

Tipo: Artigo de Revista Científica

Publicado em 29/01/2012
EN

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The present study investigated the longitudinal impact of the Project PATHS, a large-scale curriculum-based positive youth development program in Hong Kong, on the development of adolescents' risk behavior over a period of five years. Using a longitudinal randomized controlled design, eight waves of data were collected from 19 experimental schools in which students participated in the Project PATHS (N = 2,850 at Wave 8) and 24 control schools without joining the Project PATHS (N = 3,640 at Wave 8). At each wave, students responded to measures assessing their current risk behaviors, including delinquency, use of different types of drug, and their intentions of participating in risk behaviors in the future. Results demonstrated that adolescents receiving the program exhibited significantly slower increases in delinquent behaviors and substance use as compared to the control participants. During two years after the completion of the program, differences in youth risk behaviors in the two groups still existed. These results suggest that the Project PATHS has long-term effect in preventing adolescent problem behavior through promoting positive youth development.

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## Bi-banded paths, a bijection and the Narayana numbers

Fonte: University of Queensland
Publicador: University of Queensland

Tipo: Artigo de Revista Científica

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We find a bijection between bi-banded paths and peak-counting paths, applying to two classes of lattice paths including Dyck paths. Thus we find a new interpretation of Narayana numbers as coefficients of weight polynomials enumerating bi-banded Dyck path

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## Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematical Physics#Condensed Matter - Statistical Mechanics#High Energy Physics - Theory#Mathematics - Probability#Nonlinear Sciences - Exactly Solvable and Integrable Systems

As an image of the many-to-one map of loop-erasing operation $\LE$ of random
walks, a self-avoiding walk (SAW) is obtained. The loop-erased random walk
(LERW) model is the statistical ensemble of SAWs such that the weight of each
SAW $\zeta$ is given by the total weight of all random walks $\pi$ which are
inverse images of $\zeta$, $\{\pi: \LE(\pi)=\zeta \}$. We regard the Brownian
paths as the continuum limits of random walks and consider the statistical
ensemble of loop-erased Brownian paths (LEBPs) as the continuum limits of the
LERW model. Following the theory of Fomin on nonintersecting LERWs, we
introduce a nonintersecting system of $N$-tuples of LEBPs in a domain $D$ in
the complex plane, where the total weight of nonintersecting LEBPs is given by
Fomin's determinant of an $N \times N$ matrix whose entries are boundary
Poisson kernels in $D$. We set a sequence of chambers in a planar domain and
observe the first passage points at which $N$ Brownian paths $(\gamma_1,...,
\gamma_N)$ first enter each chamber, under the condition that the loop-erased
parts $(\LE(\gamma_1),..., \LE(\gamma_N))$ make a system of nonintersecting
LEBPs in the domain in the sense of Fomin. We prove that the correlation
functions of first passage points of the Brownian paths of the present system
are generally given by determinants specified by a continuous function called
the correlation kernel. The correlation kernel is of Eynard-Mehta type...

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## Confluence of geodesic paths and separating loops in large planar quadrangulations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We consider planar quadrangulations with three marked vertices and discuss
the geometry of triangles made of three geodesic paths joining them. We also
study the geometry of minimal separating loops, i.e. paths of minimal length
among all closed paths passing by one of the three vertices and separating the
two others in the quadrangulation. We concentrate on the universal scaling
limit of large quadrangulations, also known as the Brownian map, where pairs of
geodesic paths or minimal separating loops have common parts of non-zero
macroscopic length. This is the phenomenon of confluence, which distinguishes
the geometry of random quadrangulations from that of smooth surfaces. We
characterize the universal probability distribution for the lengths of these
common parts.; Comment: 48 pages, 33 color figures. Final version, with one concluding
paragraph and one reference added, and several other small corrections

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## Invariances of random fields paths, with applications in Gaussian Process Regression

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/08/2013

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#Mathematics - Statistics Theory#Mathematics - Probability#Statistics - Methodology#Statistics - Machine Learning

We study pathwise invariances of centred random fields that can be controlled
through the covariance. A result involving composition operators is obtained in
second-order settings, and we show that various path properties including
additivity boil down to invariances of the covariance kernel. These results are
extended to a broader class of operators in the Gaussian case, via the Lo\`eve
isometry. Several covariance-driven pathwise invariances are illustrated,
including fields with symmetric paths, centred paths, harmonic paths, or sparse
paths. The proposed approach delivers a number of promising results and
perspectives in Gaussian process regression.

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## A uniform estimate for rough paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We prove an extension to the classical continuity theorem in rough paths. We
show that two $p$-rough paths are close in all levels of iterated integrals
provided the first $\lfl p \rfl$ terms are close in a uniform sense.
Applications include estimation of the difference of the signatures of two
uniformly close paths and convergence rates of Gaussian rough paths.; Comment: Published at Bulletin des Sciences Math\'ematiques

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## Positive paths in the linear symplectic group

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/06/1996

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A positive path in the linear symplectic group $\Sp(2n)$ is a smooth path
which is everywhere tangent to the positive cone. These paths are generated by
negative definite (time-dependent) quadratic Hamiltonian functions on Euclidean
space. A special case are autonomous positive paths, which are generated by
time-independent Hamiltonians, and which all lie in the set $\Uu$ of
diagonalizable matrices with eigenvalues on the unit circle. However, as was
shown by Krein, the eigenvalues of a general positive path can move off the
unit circle. In this paper, we extend Krein's theory: we investigate the
general behavior of positive paths which do not encounter the eigenvalue 1,
showing, for example, that any such path can be extended to have endpoint with
all eigenvalues on the circle. We also show that in the case $2n=4$ there is a
close relation between the index of a positive path and the regions of the
symplectic group that such a path can cross. Our motivation for studying these
paths came from a geometric squeezing problem in symplectic topology. However,
they are also of interest in relation to the stability of periodic Hamiltonian
systems and in the theory of geodesics in Riemannian geometry.; Comment: Latex 26 pages

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## Semi-infinite paths of the 2d-Radial Spanning Tree

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We study semi-infinite paths of the radial spanning tree (RST) of a Poisson
point process in the plane. We first show that the expectation of the number of
intersection points between semi-infinite paths and the sphere with radius $r$
grows sublinearly with $r$. Then, we prove that in each (deterministic)
direction, there exists with probability one a unique semi-infinite path,
framed by an infinite number of other semi-infinite paths of close asymptotic
directions. The set of (random) directions in which there are more than one
semi-infinite paths is dense in $[0,2\pi)$. It corresponds to possible
asymptotic directions of competition interfaces. We show that the RST can be
decomposed in at most five infinite subtrees directly connected to the root.
The interfaces separating these subtrees are studied and simulations are
provided.; Comment: 22 pages

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## Counting Dyck paths by area and rank

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The set of Dyck paths of length $2n$ inherits a lattice structure from a
bijection with the set of noncrossing partitions with the usual partial order.
In this paper, we study the joint distribution of two statistics for Dyck
paths: \emph{area} (the area under the path) and \emph{rank} (the rank in the
lattice).
While area for Dyck paths has been studied, pairing it with this rank
function seems new, and we get an interesting $(q,t)$-refinement of the Catalan
numbers. We present two decompositions of the corresponding generating
function: one refines an identity of Carlitz and Riordan; the other refines the
notion of $\gamma$-nonnegativity, and is based on a decomposition of the
lattice of noncrossing partitions due to Simion and Ullman.
Further, Biane's correspondence and a result of Stump allow us to conclude
that the joint distribution of area and rank for Dyck paths equals the joint
distribution of length and reflection length for the permutations lying below
the $n$-cycle $(12...n)$ in the absolute order on the symmetric group.; Comment: 24 pages, 7 figures. Connections with work of C. Stump
(arXiv:0808.2822v2) eliminated the need for 5 pages of proof in the first
draft

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## Nonrepetitive Paths and Cycles in Graphs with Application to Sudoku

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/07/2005

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#Computer Science - Data Structures and Algorithms#Computer Science - Artificial Intelligence#F.2.2#I.2.1

We provide a simple linear time transformation from a directed or undirected
graph with labeled edges to an unlabeled digraph, such that paths in the input
graph in which no two consecutive edges have the same label correspond to paths
in the transformed graph and vice versa. Using this transformation, we provide
efficient algorithms for finding paths and cycles with no two consecutive equal
labels. We also consider related problems where the paths and cycles are
required to be simple; we find efficient algorithms for the undirected case of
these problems but show the directed case to be NP-complete. We apply our path
and cycle finding algorithms in a program for generating and solving Sudoku
puzzles, and show experimentally that they lead to effective puzzle-solving
rules that may also be of interest to human Sudoku puzzle solvers.; Comment: 17 pages, 11 figures

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## Combinatorics of lattice paths with and without spikes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/03/1999

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We derive a series of results on random walks on a d-dimensional hypercubic
lattice (lattice paths). We introduce the notions of terse and simple paths
corresponding to the path having no backtracking parts (spikes). These paths
label equivalence classes which allow a rearrangement of the sum over paths.
The basic combinatorial quantities of this construction are given. These
formulas are useful when performing strong coupling (hopping parameter)
expansions of lattice models. Some applications are described.; Comment: Latex. 25 pages

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## Optimal self-avoiding paths in dilute random medium

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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By a new type of finite size scaling analysis on the square lattice, and by
renormalization group calculations on hierarchical lattices we investigate the
effects of dilution on optimal undirected self-avoiding paths in a random
environment. The behaviour of the optimal paths remains the same as for
directed paths in undiluted medium, as long as forbidden bonds are not
exceeding the percolation threshold. Thus, overhanging configurations do not
alter the standard self-affine directed polymer scaling regime, even above the
directed threshold, when they become unavoidable. When dilution reaches the
undirected threshold, the optimal path becomes fractal, with fractal dimension
equal to $D_{\rm min}$, the dimension of the minimal length path on percolation
cluster backbone. In this regime the optimal path energy fluctuation,
$\overline{\Delta E}$, can be ascribed entirely to minimal length fluctuations,
and satisfies $\overline{\Delta E} \propto L^{\omega}$, with $\omega=1.02 \pm
0.06$ in $2d$, $L$ being the Euclidean distance. Hierarchical lattice
calculations confirm that $\omega$ is also the exponent of the leading scaling
correction to $\overline E \propto L^{D_{\rm min}}$.
Upon approaching threshold, the probability, ${\cal R}$, that the optimal path
does not stick entirely on the minimal length one...

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## Maximum distributions of bridges of noncolliding Brownian paths

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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#Condensed Matter - Statistical Mechanics#Condensed Matter - Soft Condensed Matter#Mathematical Physics

The one-dimensional Brownian motion starting from the origin at time $t=0$,
conditioned to return to the origin at time $t=1$ and to stay positive during
time interval $0 < t < 1$, is called the Bessel bridge with duration 1. We
consider the $N$-particle system of such Bessel bridges conditioned never to
collide with each other in $0 < t < 1$, which is the continuum limit of the
vicious walk model in watermelon configuration with a wall. Distributions of
maximum-values of paths attained in the time interval $t \in (0,1)$ are studied
to characterize the statistics of random patterns of the repulsive paths on the
spatio-temporal plane. For the outermost path, the distribution function of
maximum value is exactly determined for general $N$. We show that the present
$N$-path system of noncolliding Bessel bridges is realized as the
positive-eigenvalue process of the $2N \times 2N$ matrix-valued Brownian bridge
in the symmetry class C. Using this fact computer simulations are performed and
numerical results on the $N$-dependence of the maximum-value distributions of
the inner paths are reported. The present work demonstrates that the
extreme-value problems of noncolliding paths are related with the random matrix
theory, representation theory of symmetry...

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