Watch a 57-minute lecture exploring the mathematical concepts of the boundary-driven q-Hahn process, presented at the International Centre for Theoretical Sciences as part of a comprehensive program on discrete integrable systems. Delve into advanced topics spanning difference equations, cluster algebras, and probabilistic models, with particular focus on integrable probability and interacting particle systems. Learn from expert insights into stochastic growth models related to the KPZ equation, random tilings, and applications of quantum integrable systems. Gain understanding of the mathematical frameworks connecting theoretical physics, combinatorics, representation theory, geometry, and probability through the lens of discrete integrable systems and their conserved quantities.