Dynamical Correlations among Vicious Random Walkers

Details Dynamical Correlations among Vicious Random Walkers Dynamical Correlations among Vicious Random Walkers

2002-02-05

arxiv.org/abs/cond-mat/0202068v1

Phys. Lett. A307 (2003) 29

Physics

Condensed Matter

Statistical Mechanics

REVTeX3.1, 4 pages, no figure

Scientific paper

10.1016/S0375-9601(02)01661-4

Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin at time t=0 and then undergo mutually avoiding Brownian motion until a finite time t=T. In the short time limit $t \ll T$, the particle distribution is asymptotically described by Gaussian Unitary Ensemble (GUE) of random matrices. At the end time t = T, it is identical to that of Gaussian Orthogonal Ensemble (GOE). The Brownian motion is generally described by the dynamical correlations among particles at many times $t_1,t_2,..., t_M$ between t=0 and t=T. We show that the most general dynamical correlations among arbitrary number of particles at arbitrary number of times are written in the forms of quaternion determinants. Asymptotic forms of the correlations in the limit $N \to \infty$ are evaluated and a discontinuous transition of the universality class from GUE to GOE is observed.

Affiliated with

Also associated with

No associations

Rating

Dynamical Correlations among Vicious Random Walkers 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 Dynamical Correlations among Vicious Random Walkers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical Correlations among Vicious Random Walkers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-705005