Stationary distributions of systems with discreteness-induced transitions | Zendy

Enrico Bibbona | Zendy; Jinsu Kim | Zendy; Carsten Wiuf | Zendy

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Stationary distributions of systems with discreteness-induced transitions

Author(s) -

Enrico Bibbona,

Jinsu Kim,

Carsten Wiuf

Publication year - 2020

Publication title -

journal of the royal society interface

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.655

H-Index - 139

eISSN - 1742-5689

pISSN - 1742-5662

DOI - 10.1098/rsif.2020.0243

Subject(s) - ergodicity , statistical physics , scaling , mathematics , stationary state , stationary distribution , volume (thermodynamics) , chain (unit) , physics , quantum mechanics , markov chain , statistics , geometry

We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discreteness-induced transitions. The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution and discuss the effect of volume scaling on the stationary behaviour of the chain. We find the exact critical value of the volume for which discreteness-induced transitions disappear.

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