Probability Seminar: Augusto Teixeira

During this talk we will introduce a method, called 'soft local times', to couple the trace of two Markov chains running on the same state space. This method is general and can give non-trivial bounds for several models of interest. We then give a particularly useful example of application involving the model of random interlacements on Z^d. For that, we will first introduce this process in detail and show how the method of soft local times can help decoupling the random interlacements in two separated sets. An interesting consequence of such result is the exponential decay of the connectivity function for d > 3.