Asymptotic analysis for stationary distributions of multiscaled reaction networks

Hoessly, Linard, Wiuf, Carsten and Xia, Panqiu 2025. Asymptotic analysis for stationary distributions of multiscaled reaction networks. Advances in Applied Probability 10.1017/apr.2025.10040

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Abstract

We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and the reduction of such networks by assuming that a set of species (called non-interacting species) are degraded fast (and therefore essentially absent from the network), implying that some reaction rates are large relative to others. Technically, we assume that these reaction rates are scaled by a common parameter N and let . The limiting stationary distribution as is compared with the stationary distribution of the reduced reaction network obtained by elimination of the non-interacting species. In general, the limiting stationary distribution could differ from the stationary distribution of the reduced reaction network. We identify various sufficient conditions under which these two distributions are the same, including when the reaction network is detailed balanced and when the set of non-interacting species consists of intermediate species. In the latter case, the limiting stationary distribution essentially retains the form of the complex balanced distribution. This finding is particularly surprising given that the reduced reaction network could be non-weakly reversible and might exhibit unconventional kinetics.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Applied Probability Trust
ISSN:	0001-8678
Date of First Compliant Deposit:	16 December 2025
Date of Acceptance:	13 October 2025
Last Modified:	16 Dec 2025 10:45
URI:	https://orca.cardiff.ac.uk/id/eprint/183276

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