Vertex Model Integrability for Stochastic Particle Systems

Explore a 51-minute lecture on vertex model integrability for stochastic particle systems presented by Leonid Petrov from the University of Virginia at IPAM's Vertex Models workshop. Delve into the study of integrable stochastic particle systems in one space dimension, focusing on examples like the Totally Asymmetric Simple Exclusion process (TASEP). Discover how these systems balance mathematical tractability with the ability to describe complex phenomena. Examine the generalization of questions about these systems through the introduction of multiple parameters and the interpretation of particle system time evolution as vertex model transfer matrices. Investigate applications of vertex models and their associated Yang-Baxter equations to stochastic systems, gaining insights into this field that has been studied for over 50 years since its introduction in biology and mathematics in 1969-70.