TY - JOUR

T1 - Large fluctuations in stochastic population dynamics

T2 - Momentum-space calculations

AU - Assaf, Michael

AU - Meerson, Baruch

AU - Sasorov, Pavel V.

PY - 2010/7

Y1 - 2010/7

N2 - 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.

AB - 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.

KW - Large deviations in non-equilibrium systems

KW - Metastable states

KW - Population dynamics (theory)

KW - Stochastic particle dynamics (theory)

UR - http://www.scopus.com/inward/record.url?scp=77957090337&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2010/07/P07018

DO - 10.1088/1742-5468/2010/07/P07018

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AN - SCOPUS:77957090337

SN - 1742-5468

VL - 2010

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 7

M1 - P07018

ER -