Learn about the latest developments in Markov-chain algorithms and their applications in this advanced lecture delivered at the Galileo Galilei Institute. Explore cutting-edge concepts in the second installment of a series focusing on the revolutionary advances in Markov-chain methodology. Delve into theoretical frameworks and practical implementations that characterize what is being called the "second revolution" in Markov-chain development. Gain insights from Professor Werner Krauth's expertise as he presents complex mathematical concepts and their implications for modern computational methods over the course of 105 minutes.