@article{ACFK2025,
 abstract = {This paper provides a new path method that can be used to determine when an ergodic continuous-time Markov chain on $\mathbb{Z}^d$ converges exponentially fast to its stationary distribution in $L^2$. Specifically, we provide general conditions that guarantee the positivity of the spectral gap. Importantly, our results do not require the assumption of time-reversibility of the Markov model. We then apply our new method to the well-studied class of stochastically modeled reaction networks. Notably, we show that each complex-balanced model that is also 'open' has a positive spectral gap, and is therefore exponentially ergodic. We further illustrate how our results can be applied for models that are not necessarily complex-balanced. Moreover, we provide an example of a detailed-balanced (in the sense of reaction network theory), and hence complex-balanced, stochastic reaction network that is not exponentially ergodic. We believe this to be the first such example in the literature.},
 author = {Anderson, David F. and Cappelletti, Daniele and Fan, Wai-Tong Louis and Kim, Jinsu},
 doi = {10.1137/24M1665933},
 journal = {SIAM Journal on Applied Dynamical Systems},
 keywords = {continuous time Markov chains; spectral gap; exponential ergodicity; stochastic reaction networks; complex-balanced systems},
 month = {06},
 number = {2},
 pages = {1668--1710},
 publisher = {SIAM},
 title = {A New Path Method for Exponential Ergodicity of Markov Processes on $\mathbb{Z}^d$, with Applications to Stochastic Reaction Networks},
 url = {https://doi.org/10.1137/24M1665933},
 volume = {24},
 year = {2025}
}