Scaling limit of vicious walks and two-matrix model

Makoto Katori, Hideki Tanemura

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Abstract

We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of N particles is studied and it is described by use of the probability density function of eigenvalues of [formula presented] Gaussian random matrices. The particle distribution depends on the ratio of the observation time t and the time interval T in which the nonintersecting condition is imposed. As [formula presented] is going on from 0 to 1, there occurs a transition of distribution, which is identified with the transition observed in the two-matrix model of Pandey and Mehta. Despite of the absence of matrix structure in the original vicious walker model, in the diffusion scaling limit, accumulation of contact repulsive interactions realizes the correlated distribution of eigenvalues in the multimatrix model as the particle distribution.

Original languageEnglish
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume66
Issue number1
DOIs
Publication statusPublished - 2002 Jul 22
Externally publishedYes

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

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