Coexistence and duality in competing species models
Probability
2018-11-26 v3
Abstract
We discuss some stochastic spatial generalizations of the Lotka--Volterra model for competing species. The generalizations take the forms of spin systems on general discrete sets and interacting diffusions on integer lattices. Methods for proving coexistence in these generalizations and some related open questions are discussed. We use duality as the central point of view. It relates coexistence of the models to survival of their dual processes.
Keywords
Cite
@article{arxiv.1802.10476,
title = {Coexistence and duality in competing species models},
author = {Yu-Ting Chen and Matthias Hammer},
journal= {arXiv preprint arXiv:1802.10476},
year = {2018}
}
Comments
27 pages. This article is based on lecture notes for the learning session 'Competing species models' given by the authors and held during July and August, 2017 in the Institute for Mathematical Sciences at the National University of Singapore