A random walk with catastrophes
Probability
2019-03-13 v1
Abstract
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population dynamics with linear growth and binomial catastrophes: in a catastrophe, each individual survives with some fixed probability, independently of the rest. Through a coupling construction, we obtain sharp two-sided bounds for the rate of convergence to stationarity which are applied to show that the model exhibits a cutoff phenomenon.
Cite
@article{arxiv.1709.04780,
title = {A random walk with catastrophes},
author = {Iddo Ben-Ari and Alexander Roitershtein and Rinaldo B. Schinazi},
journal= {arXiv preprint arXiv:1709.04780},
year = {2019}
}