Spectral theory of metastability and extinction in birth-death systems

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.

4 pages, 3 figures

References in corpus (3)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Spectral formulation and WKB approximation for rare-event statistics in reaction systems
• Stochastic resonance due to internal noise in reaction kinetics

Cited by in corpus (4)

• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Quasi-stationary regime of a branching random walk in presence of an absorbing wall
• Persistence of instanton connections in chemical reactions with time dependent rates
• Efficient Stochastic Simulations of Complex Reaction Networks on Surfaces