Entropy and Curvature of Markov Chains on Metric Spaces

Explore the Peres-Tetali conjecture and its implications for Markov chains in this 57-minute lecture by Justin Salez from the Hausdorff Center for Mathematics. Delve into the relationship between contraction in Wasserstein distance and relative entropy for Markov chains on metric spaces. Begin with a historical overview of the conjecture, then examine the main results presented by Salez and his collaborators. Gain insights into various applications of this research, which stems from joint works with Pietro Caputo and Florentin Münch. Enhance your understanding of entropy, curvature, and the intricate properties of Markov chains in metric spaces through this in-depth mathematical exploration.