Dynamical correlations for vicious random walk with a wall Original Research Article

A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisherʹs 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→∞, 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.