Quantitative spectral gaps and uniform lower bounds in the small noise limit for Markov semigroups generated by hypoelliptic stochastic differential equations

Jacob Bedrossian, Kyle Liss

We study the convergence rate to equilibrium for a family of Markov semigroups $\{{\mathcal{P}}_t^{\epsilon }{\}}_{\epsilon >0}$ generated by a class of hypoelliptic stochastic differential equations o…