Giant disparity and a dynamical phase transition in large deviations of the time-averaged size of stochastic populations

Pini Zilber, Naftali R. Smith, Baruch Meerson

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study large deviations of the time-averaged size of stochastic populations described by a continuous-time Markov jump process. When the expected population size N in the steady state is large, the large deviation function (LDF) of the time-averaged population size can be evaluated by using a Wentzel-Kramers-Brillouin (WKB) method, applied directly to the master equation for the Markov process. For a class of models that we identify, the direct WKB method predicts a giant disparity between the probabilities of observing an unusually small and an unusually large values of the time-averaged population size. The disparity results from a qualitative change in the "optimal" trajectory of the underlying classical mechanics problem. The direct WKB method also predicts, in the limit of N→∞, a singularity of the LDF, which can be interpreted as a second-order dynamical phase transition. The transition is smoothed at finite N, but the giant disparity remains. The smoothing effect is captured by the van-Kampen system size expansion of the exact master equation near the attracting fixed point of the underlying deterministic model. We describe the giant disparity at finite N by developing a different variant of WKB method, which is applied in conjunction with the Donsker-Varadhan large-deviation formalism and involves subleading-order calculations in 1/N.

Original languageEnglish
Article number052105
JournalPhysical Review E
Volume99
Issue number5
DOIs
StatePublished - 6 May 2019
Externally publishedYes

Fingerprint

Dive into the research topics of 'Giant disparity and a dynamical phase transition in large deviations of the time-averaged size of stochastic populations'. Together they form a unique fingerprint.

Cite this