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2019 A random walk with catastrophes
Iddo Ben-Ari, Alexander Roitershtein, Rinaldo B. Schinazi
Electron. J. Probab. 24: 1-21 (2019). DOI: 10.1214/19-EJP282


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. "A random walk with catastrophes." Electron. J. Probab. 24 1 - 21, 2019.


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

zbMATH: 07055666
MathSciNet: MR3933207
Digital Object Identifier: 10.1214/19-EJP282

Primary: 60J10 , 60J80
Secondary: 60K37 , 92D25

Keywords: catastrophes , coupling , Cutoff , Persistence , population models , spectral gap


Vol.24 • 2019
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