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Spectral theory of metastability and extinction in birth-death systems

Michael Assaf·Baruch Meerson
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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.

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Michael Assaf, Baruch Meerson. 2006-10-24. Spectral theory of metastability and extinction in birth-death systems. https://doi.org/10.1103/physrevlett.97.200602

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