Hypocoercivity with Schur complements

These preliminary notes describe the approach presented by Gabriel Stoltz at the workshop on hypocoercivity at the Heilbronn Institute for Mathematical Research in Bristol, UK (3-4 March 2020). We present an approach to obtaining directly 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).