Two-Sided Infinite Systems of Competing Brownian Particles
Probability
2017-06-19 v6
Abstract
Two-sided infinite systems of Brownian particles with rank-dependent dynamics, indexed by all integers, exhibit different properties from their one-sided infinite counterparts, indexed by positive integers, and from finite systems. Consider the gap process, which is formed by spacings between adjacent particles. In stark contrast with finite and one-sided infinite systems, two-sided infinite systems can have one- or two-parameter family of stationary gap distributions, or the gap process weakly converging to zero as time goes to infinity.
Keywords
Cite
@article{arxiv.1509.01859,
title = {Two-Sided Infinite Systems of Competing Brownian Particles},
author = {Andrey Sarantsev},
journal= {arXiv preprint arXiv:1509.01859},
year = {2017}
}
Comments
32 pages. Keywords: Competing Brownian particles, gap process, weak convergence, stationary distribution, named particles, ranked particles, stochastic domination, interacting particle systems