Dynamical Correlations for Vicious Random Walk with a Wall

Abstract

A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. $N$ Brownian particles start from the origin at time $t=0$ and undergo mutually avoiding motion until a finite time $t=T$. Dynamical correlation functions among the walkers are exactly evaluated in the case with a wall at the origin. Taking an asymptotic limit $N\to \infty$, we observe discontinuous transitions in the dynamical correlations. It is further shown that the vicious walk model with a wall is equivalent to a parametric random matrix model describing the crossover between the Bogoliubov-deGennes universality classes.

LaTeX, 21 pages, no figure, minor corrections made before publication in Nucl. Phys. B

References in corpus (3)

• Scaling limit of vicious walks and two-matrix model
• Dynamical Correlations among Vicious Random Walkers
• Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles

Cited by in corpus (12)

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• Noncolliding Brownian Motion and Determinantal Processes
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• Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
• Functional central limit theorems for vicious walkers
• Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals
• Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
• Pfaffian Expressions for Random Matrix Correlation Functions
• The hard-edge tacnode process for Brownian motion
• Determinantal process starting from an orthogonal symmetry is a Pfaffian process
• Characteristic Polynomials of Random Matrices and Noncolliding Diffusion Processes