Event-chain algorithms: taming randomness in Monte Carlo methods through irreversibility, factorization and lifting

I will first present the irreversible and rejection-free Monte Carlo methods recently developed in Physics under the name Event-Chain. They have proven to produce clear acceleration over standard Monte Carlo methods, thanks to the reduction of their random-walk behavior. Their irreversible nature relies on three key ingredients: the factorized filter, the generalized lifting framework and the infinitesimal moves.  Then, I will focus on the new Forward Event-Chain version that allows to reduce the randomization needed for ergodicity, leading to a striking speed-up. Finally, I will explain how the factorized filter may be the key to subsampling in Monte Carlo methods.