Stationary distributions and condensation in autocatalytic CRN

TL;DR

This paper derives explicit steady-state distributions for a broad class of non-weakly reversible autocatalytic reaction networks, enabling analysis of condensation phenomena in generalized particle systems with applications across various scientific fields.

Contribution

It provides the first explicit product-form steady-state distributions for non-weakly reversible autocatalytic CRNs of arbitrary deficiency, expanding understanding beyond traditional weakly reversible assumptions.

Findings

Explicit product-form steady-state distributions derived

Condensation phenomena analyzed in generalized particle systems

Applications demonstrated in statistical mechanics, life sciences, and robotics

Abstract

We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first give explicitly product-form steady-state distributions for a class of non weakly reversible autocatalytic CRN of arbitrary deficiency. Examples of interest in statistical mechanics (inclusion process), life sciences and robotics (collective decision making in ant and robot swarms) are provided. The product-form nature of the steady-state then enables the study of condensation in particle systems that are generalizations of the inclusion process.