A random walk with catastrophes
Copyright policy )A random walk with catastrophes
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.
- University of Colorado Colorado Springs United States
- University of Colorado System United States
- Texas A&M University United States
- The University of Texas System United States
- University of Connecticut United States
60J80, population models, Probability (math.PR), persistence, 92D25, catastrophes, Markov chains (discrete-time Markov processes on discrete state spaces), 60K37, Population dynamics (general), Branching processes (Galton-Watson, birth-and-death, etc.), spectral gap, FOS: Mathematics, 60J10, cutoff, Processes in random environments, coupling, Mathematics - Probability
60J80, population models, Probability (math.PR), persistence, 92D25, catastrophes, Markov chains (discrete-time Markov processes on discrete state spaces), 60K37, Population dynamics (general), Branching processes (Galton-Watson, birth-and-death, etc.), spectral gap, FOS: Mathematics, 60J10, cutoff, Processes in random environments, coupling, Mathematics - Probability
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