Article

Stationary distributions of systems with Discreteness Induced Transitions

Enrico BibbonaPolytechnic University of TurinJinsu KimDepartment of Mathematics , University of California , Irvine, CA, USACarsten WiufDepartment of Mathematical Sciences University of Copenhagen Copenhagen Denmark

Research at the University of Copenhagen (University of Copenhagen)repository2020en

ABI

Abstract

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.

Topics

Advanced Thermodynamics and Statistical Mechanics

Identifiers

DOI: 10.1098/rsif.2020.0243rsif20200243

Citations and references

Cited by 00 references

Metrics — AkademScholar · Coming soon