On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms

We establish $L^2$-exponential convergence rate for three popular piecewise deterministic Markov processes sampling: the randomized Hamiltonian Monte Carlo method, zigzag process, and bouncy particle sampler. Our analysis is based on a variational framework hypocoercivity, which combines Poincar\'{e}-type inequality in time-augmented state space standard $L^2$ energy estimate. provides explicit estimates, are more quantitative than existing results.