# Metastability of a random walk with catastrophes

## TL;DR

This paper investigates the metastable behavior of a population model represented by a random walk with catastrophes, analyzing its long-term persistence and phase transitions as parameters approach extreme values.

## Contribution

It introduces four new limiting regimes that elucidate the metastable phase of the process under extreme parameter conditions.

## Key findings

- Identification of four different limiting behaviors of the process.
- Insights into the persistence duration before absorption at zero.
- Enhanced understanding of phase transitions in population models.

## Abstract

We consider a random walk with catastrophes which was introduced to model population biology. It is known that this Markov chain gets eventually absorbed at $0$ for all parameter values. Recently, it has been shown that this chain exhibits a metastable behavior in the sense that it can persist for a very long time before getting absorbed. In this paper we study this metastable phase by making the parameters converge to extreme values. We obtain four different limits that we believe shed light on the metastable phase.