Year: 2011
Type: preprint
Abstract: We consider the noncolliding Brownian motion (BM) with $N$ particles starting from the eigenvalue distribution of Gaussian unitary ensemble (GUE) of $N \times N$ Hermitian random matrices with variance $σ^2$. We prove that this process is equivalent with the time shift $t \to t+σ^2$ of the noncolliding BM starting from the configuration in which all $N$ particles are put at the origin. In order to demonstrate nontriviality of such equivalence for determinantal processes, we show that, even from its special consequence, determinantal expressions are derived for the ensemble averages of products of characteristic polynomials of random matrices in GUE. Another determinantal process, noncolliding squared Bessel process with index $ν>-1$, is also studied in parallel with the noncolliding BM and corresponding results for characteristic polynomials are given for random matrices in the chiral GUE as well as in the Gaussian ensembles of class C and class D.
Source: arXiv (Cornell University)
Author: Katori, Makoto
Institution: Chuo University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2123889770