Hypocoercivity with Schur complements
Résumé
We propose an approach to directly obtaining estimates on the resolvent of hypocoercive operators, using Schur complements, rather than obtaining bounds on the resolvent from an exponential decay of the evolution semigroup. We present applications to Langevin-like dynamics and Fokker--Planck equations, as well as the linear Boltzmann equation (which is also the generator of randomized Hybrid Monte Carlo in molecular dynamics). In particular, we make precise the dependence of the resolvent bounds on the parameters of the dynamics and on the dimension. We also highlight relationships with other hypocoercive approaches.