Résumé : During this talk, I will present how the development of non-reversible algorithms by piecewise deterministic Markov processes (PDMP) was first motivated by the impressive successes of cluster algorithms for the simulation of lattice spin systems. I will especially stress how the spin involution symmetry crucial to the cluster schemes was replaced by the exploitation of more general symmetry, in particular thanks to the factorization of the energy function.

Keywords : Monte Carlo methods; Metropolis algorithm; factorized Metropolis filter; particle systems; Markov chain lifting; Markov-chain Monte Carlo algorithms; event-chain Monte Carlo; lifting; global balance condition