BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Minjoon Kim (POSTECH) DTSTART:20240314T163000Z DTEND:20240314T170000Z DTSTAMP:20260421T124519Z UID:MoRN/95 DESCRIPTION:Title: A path method for non-exponential ergodicity of Markov chains and its applic ation for chemical reaction systems\nby Minjoon Kim (POSTECH) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe prese nt criteria for non-exponential ergodicity of continuous-time Markov chain s on a countable state space. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this path met hod to explore the non-exponential convergence of microscopic biochemical interacting systems. Using reaction network descriptions\, we identified s pecial architectures of biochemical systems for non-exponential ergodicity . In essence\, we found that reactions forming a cycle in the reaction net work can induce non-exponential ergodicity when they significantly dominat e other reactions across infinitely many regions of the state space. Inter estingly\, special architectures allowed us to construct many detailed bal anced and complex balanced biochemical systems that are non-exponentially ergodic. Some of these models are low-dimensional bimolecular systems with few reactions. Thus this work suggests the possibility of discovering or synthesizing stochastic systems arising in biochemistry that possess eithe r detailed balancing or complex balancing and slowly\nconverges to their s tationary distribution.\n LOCATION:https://researchseminars.org/talk/MoRN/95/ END:VEVENT END:VCALENDAR