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arXiv · 1709.04780

A random walk with catastrophes

Iddo Ben-Ari·Alexander Roitershtein·Rinaldo B. Schinazi
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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.

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Iddo Ben-Ari, Alexander Roitershtein, Rinaldo B. Schinazi. 2017-09-14. A random walk with catastrophes. https://arxiv.org/abs/1709.04780

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