Quantitative ergodicity for gene regulatory networks with transcriptional bursting
Probability
2026-05-12 v1 Molecular Networks
Abstract
We study the long-term behavior of two piecewise-deterministic Markov processes used to model stochastic gene regulatory networks with bursting dynamics. Under regularity assumptions on the jump rate, we prove the existence and uniqueness of the stationary distribution for an arbitrary number of interacting genes and an arbitrary strength of interaction. Using coupling methods, we also provide explicit upper bounds for the convergence to equilibrium in terms of Wasserstein distances.
Keywords
Cite
@article{arxiv.2605.08345,
title = {Quantitative ergodicity for gene regulatory networks with transcriptional bursting},
author = {Mathilde Gaillard and Ulysse Herbach},
journal= {arXiv preprint arXiv:2605.08345},
year = {2026}
}