On a new proof of the Harris ergodic theorem and related subexponential convergence results

Abstract

We revisit a result in probability known as the Harris theorem and give a simple proof which is well-suited for some applications in PDE. The proof is not far from the ideas of Hairer \& Mattingly (2011) but avoids the use of mass transport metrics and can be readily extended to cases where there is no spectral gap and exponential relaxation to equilibrium does not hold. We will also discuss some contexts where this result can be useful, particularly in a model for neuron populations structured by the elapsed time since the last discharge. This talk is based on joint works with Stéphane Mischler and Havva Yolda.Non UBCUnreviewedAuthor affiliation: Universidad de GranadaFacult