Julien Moy

For several probabilistic models of random surfaces, a central problem is to understand the typical rate of convergence to equilibrium for the heat flow, or the mixing rate of the geodesic flow. Explicit rates usually follow from the existence of a spectral gap -- either for the first eigenvalue of the Laplacian or for the dynamical resonances -- combined with resolvent estimates. I will present results obtained for a model of random coverings of a fixed negatively curved surface.