Explore an innovative Markov chain Monte Carlo algorithm called Ex2MCMC in this 35-minute conference talk by Eric Moulines from Ecole Polytechnique. Delve into the development of this massively parallelizable and computationally efficient method that combines multiple global proposals with mobile moves. Learn about the algorithm's V-uniform geometric ergodicity under realistic conditions and understand the explicit bounds on mixing rates that demonstrate improvements due to multiple global moves. Discover how Ex2MCMC allows for fine-tuning of exploitation (local moves) and exploration (global moves) through a novel approach to proposing dependent global moves. Examine the adaptive scheme, FlEx2MCMC, which learns the distribution of global trains using normalizing flows. Gain insights into the efficiency of Ex2MCMC and its adaptive versions through various classical sampling benchmarks, and see how these algorithms enhance the quality of sampling GANs as energy-based models.