Large fluctuations in stochastic population dynamics: Momentum-space calculations

Michael Assaf*, Baruch Meerson, Pavel V. Sasorov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


Momentum-space representation provides an interesting perspective on the theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the probability distribution of the population size is transformed into an evolution equation for the probability generating function. Spectral decomposition then yields an eigenvalue problem for a non-Hermitian linear differential operator. The ground-state eigenmode encodes the stationary distribution of the population size. For long-lived metastable populations which exhibit extinction or escape to another metastable state, the quasi-stationary distribution and the mean time to extinction or escape are encoded by the eigenmode and eigenvalue of the lowest excited state. If the average population size in the stationary or quasi-stationary state is large, the corresponding eigenvalue problem can be solved via the WKB approximation amended by other asymptotic methods. We illustrate these ideas in several model examples.

Original languageAmerican English
Article numberP07018
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number7
StatePublished - Jul 2010


  • Large deviations in non-equilibrium systems
  • Metastable states
  • Population dynamics (theory)
  • Stochastic particle dynamics (theory)


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