Recently, Markov-chain Monte Carlo methods based on non-reversible piecewise deterministic Markov processes (PDMP) are under growing attention, thanks to the increase in performance they usually bring. Beyond their numerical efficacy, the non-reversible and piecewise deterministic characteristics of these processes prompt interesting questions, regarding for instance ergodicity proof and convergence bounds. During this talk, I will particularly focus on the obtained results and open problems left while considering PDMP evolution of particle systems, both in an equilibrium and out-of-equilibrium setting. Hardcore particle systems have embodied a testbed of choice since the first implementations of Markov chain Monte Carlo in the 50’s. Even today, the entropic barriers they exhibit are still resisting to the state-of-the-art MCMC sampling methods. During this talk, I will review the recent developments regarding sampling such systems and discuss the dynamical bottlenecks that are yet to be solved.
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