Elliptic Determinantal Process of Type A
Abstract
We introduce an elliptic extension of Dyson's Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant evaluations related to the reduced affine root system of types , we give determinantal martingale representation (DMR) for the process, when it is started at the configuration with equidistant spacing on the circle. DMR proves that the process is determinantal and the spatio-temporal correlation kernel is determined. By taking temporally homogeneous limits of the present elliptic determinantal process, trigonometric and hyperbolic versions of noncolliding diffusion processes are studied.
Cite
@article{arxiv.1311.4146,
title = {Elliptic Determinantal Process of Type A},
author = {Makoto Katori},
journal= {arXiv preprint arXiv:1311.4146},
year = {2015}
}
Comments
v5: AMS-LaTeX, 35 pages, no figure, references updated for publication in Probab. Theory Relat. Fields