  The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov Chain algorithm to
sample from a target density known up to a multiplicative constant. This method
is based on a kinetic piecewise deterministic Markov process for which the
target measure is invariant. This paper deals with theoretical properties of
BPS. First, we establish geometric ergodicity of the associated semi-group
under weaker conditions than in [10] both on the target distribution and the
velocity probability distribution. This result is based on a new coupling of
the process which gives a quantitative minorization condition and yields more
insights on the convergence. In addition, we study on a toy model the
dependency of the convergence rates on the dimension of the state space.
Finally, we apply our results to the analysis of simulated annealing algorithms
based on BPS.
