Spectral theory of metastability and extinction in birth-death systems

TL;DR

This paper introduces a spectral method to accurately analyze extinction probabilities and metastable states in complex birth-death processes and chemical reactions, demonstrated on binary annihilation and triple branching examples.

Contribution

A novel spectral approach for calculating extinction statistics and quasi-stationary distributions in multi-step birth-death and chemical reaction systems.

Findings

Accurate extinction probability calculations

Effective analysis of metastable states

Application to dissociation-recombination reactions

Abstract

We suggest a general spectral method for calculating statistics of multi-step birth-death processes and chemical reactions of the type mA->nA (m and n are positive integers) which possess an absorbing state. The method yields accurate results for the extinction statistics, and for the quasi-stationary probability distribution, including large deviations, of the metastable state. The power of the method is demonstrated on the example of binary annihilation and triple branching 2A->0 and A->3A, representative of the rather general class of dissociation-recombination reactions.