Electronic Journal of Probability

A random walk with catastrophes

Iddo Ben-Ari, Alexander Roitershtein, and Rinaldo B. Schinazi

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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.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 28, 21 pp.

Received: 30 August 2018
Accepted: 25 February 2019
First available in Project Euclid: 26 March 2019

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Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 92D25: Population dynamics (general) 60K37: Processes in random environments

population models catastrophes persistence spectral gap cutoff coupling

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Ben-Ari, Iddo; Roitershtein, Alexander; Schinazi, Rinaldo B. A random walk with catastrophes. Electron. J. Probab. 24 (2019), paper no. 28, 21 pp. doi:10.1214/19-EJP282. https://projecteuclid.org/euclid.ejp/1553565779

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