A random walk with catastrophes
Iddo Ben-Ari, Alexander Roitershtein, Rinaldo B. Schinazi
TL;DR
This paper analyzes an ergodic population model with linear growth and binomial catastrophes, providing bounds on convergence rates and demonstrating a cutoff phenomenon.
Contribution
It introduces a coupling method to derive sharp bounds on the convergence rate and reveals the cutoff phenomenon in the population dynamics model.
Findings
Sharp two-sided bounds for convergence rate
Demonstration of cutoff phenomenon in the model
Analysis of population survival probabilities
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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