Geometric Functional Inequalities for Markov Chains - Mini-Course

Explore a comprehensive two-hour mini-course lecture on Geometric Functional Inequalities for Markov Chains, delivered by Dr. Sam Power from the University of Bristol at the Isaac Newton Institute. Gain insights into the functional-analytic approach to analyzing long-term Markov process behavior, complementing traditional probabilistic techniques. Learn about standard functional inequalities, their applications, and practical implementations, particularly in reversible diffusion processes and discrete-time Markov chains. Discover how these mathematical concepts apply specifically to MCMC algorithms, with the first part focusing on classical cases of reversible diffusion processes and the second part examining discrete-time Markov chains. Benefit from a carefully curated selection of references that will enable independent exploration of functional inequalities literature. Perfect for mathematicians and researchers who are familiar with probabilistic techniques but want to expand their analytical toolkit with functional-analytic approaches.