A generalised Airy distribution function for the accumulated area swept by $N$ vicious Brownian paths
Statistical Mechanics
2015-08-13 v2 Mathematical Physics
math.MP
Abstract
In this work exact expressions for the distribution function of the accumulated area swept by reunions and meanders of vicious Brownian particles up to time are derived. The results are expressed in terms of a generalised Airy distribution function, containing the Vandermonde determinant of the Airy roots. By mapping the problem to an Random Matrix Theory ensemble we are able to perform Monte Carlo simulations finding perfect agreement with the theoretical results.
Keywords
Cite
@article{arxiv.1507.03203,
title = {A generalised Airy distribution function for the accumulated area swept by $N$ vicious Brownian paths},
author = {Isaac Pérez Castillo and Denis Boyer},
journal= {arXiv preprint arXiv:1507.03203},
year = {2015}
}
Comments
18 pages