Asymptotics for the heat kernel in multicone domains

Artículo de publicación ISIA multicone domain Omega subset of R-n is an open, connected set that resembles a finite collection of cones far away from the origin. We study the rate of decay in time of the heat kernel p(t, x, y) of a Brownian motion killed upon exiting Omega, using both probabilistic and analytical techniques. We find that the decay is polynomial and we characterize lim(t ->infinity)p(t, x, y) in terms of the Martin boundary of Omega at infinity, where alpha > 0 depends on the geometry of Omega. We next derive an analogous result for t(kappa/2)P(x) (T > t), with kappa = 1 +alpha-n/2, where T is the exit time from Omega. Lastly, we deduce the renormalized Yaglom limit for the process conditioned on survival.FONDECYT 3130724 Programa Iniciativa Cientifica Milenio grant through Nucleus Millenium Stochastic Models of Complex and Disordered Systems NC13006