Scaling limit of vicious walks and two-matrix model

Details Scaling limit of vicious walks and two-matrix model Scaling limit of vicious walks and two-matrix model

2002-03-27

arxiv.org/abs/cond-mat/0203549v3

Phys. Rev. E 66 (2002) 011105

Physics

Condensed Matter

Statistical Mechanics

REVTeX4, 12 pages, no figure, minor corrections made for publication

Scientific paper

10.1103/PhysRevE.66.011105

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 $N \times N$ 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 $t/T$ 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.

Affiliated with

Also associated with

No associations

Rating

Scaling limit of vicious walks and two-matrix model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Scaling limit of vicious walks and two-matrix model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scaling limit of vicious walks and two-matrix model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-237829