5 papers
Classification for dynamics of Markov chains on non-negative integers with arbitrary transition rates and its application
Minjun Kim, Seokhwan Moon, Jinsu Kim
Continuous-time Markov chains on non-negative integers can be used for modeling biological systems, population dynamics, and queueing models. Qualitative behaviors of birth-and-dea…
A reaction network model of microscale liquid-liquid phase separation reveals effects of spatial dimension
Jinyoung Kim, Sean D. Lawley, Jinsu Kim
Proteins can form droplets via liquid-liquid phase separation (LLPS) in cells. Recent experiments demonstrate that LLPS is qualitatively different on two-dimensional (2d) surfaces…
Boundary-induced slow mixing for Markov chains and its application to stochastic reaction networks
Wai-Tong Louis Fan, Jinsu Kim, Chaojie Yuan
Markov chains on the non-negative quadrant of dimension are often used to model the stochastic dynamics of the number of entities, such as chemical species in stochasti…
A path method for non-exponential ergodicity of Markov chains and its application for chemical reaction systems
Minjoon Kim, Jinsu Kim
In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space. These criteria can be verified by examining the ratio…
A new path method for exponential ergodicity of Markov processes on , with applications to stochastic reaction networks
David F. Anderson, Daniele Cappelletti, Wai-Tong Louis Fan +1
This paper provides a new path method that can be used to determine when an ergodic continuous-time Markov chain on converges exponentially fast to its stationary dis…