LA Probability Forum

Will be held at UCLA - talks in Math Sciences Room 6627

Random interlacements is a Poissonian soup of doubly-infinite random walk trajectories on Z^d. A parameter u > 0 controls the intensity of the Poisson point process. In a natural way, the model defines percolation on the edges of Z^d with long-range correlations. We consider the time constant associated to the chemical distance in random interlacements at low intensity u > 0. It is conjectured that the time constant times u^{1/2} converges to the Euclidean norm. We prove a sharp upper bound (of order u^{-1/2}) and an almost sharp lower bound (of order u^{-1/2+\epsilon}) for the time constant as the intensity decays to zero. Joint work with Sarai Hernandez-Torres and Ron Rosenthal.