Spectral theory of metastability and extinction in birth-death systems

Michael Assaf*, Baruch Meerson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

82 Scopus citations


We suggest a general spectral method for calculating the statistics of multistep birth-death processes and chemical reactions of the type mA→nA (m and n are positive integers) which possess an absorbing state. The method employs the generating function formalism in conjunction with the Sturm-Liouville theory of linear differential operators. It yields accurate results for the extinction statistics and for the quasistationary 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→, A→3A, representative of the rather general class of dissociation-recombination reactions.

Original languageAmerican English
Article number200602
JournalPhysical Review Letters
Issue number20
StatePublished - 2006


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