Spectral theory of metastability and extinction in birth-death systems

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  • 16 October 2006
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 method is demonstrated by an example of binary annihilation and triple branching 2A->0 and A->3A, describing, for example, a dissociation-recombination reaction.

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