Spectral theory of metastability and extinction in birth-death systems

Details Spectral theory of metastability and extinction in birth-death systems Spectral theory of metastability and extinction in birth-death systems

2006-10-16

arxiv.org/abs/cond-mat/0610415v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.97.200602

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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