An algebraic approach to product-form stationary distributions for some reaction networks
arXiv:2012.03227 · doi:10.1137/21M1401498
Abstract
Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative ergodic CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.
arXiv commentAccepted for publication in SIAM Journal on Applied Dynamical Systems
References in corpus (12)
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Duality and hidden symmetries in interacting particle systems
- Markovian Dynamics on Complex Reaction Networks
- Condensation in the inclusion process and related models
- Product-form Poisson-like distributions and complex balanced reaction systems
- Condensation in stochastic particle systems with stationary product measures
- Dynamics of condensation in the totally asymmetric inclusion process
- Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics
- A mass transport model with a simple non-factorized steady-state distribution
- Stationary distributions via decomposition of stochastic reaction networks
- Motif Analysis for Small-Number Effects in Chemical Reaction Dynamics
- The asymptotic tails of limit distributions of continuous time Markov chains