Abstract: Random interlacements (RI) 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. The model defines a long-range percolation on the edges of Z^d, called the random interlacements graph, composed of those edges traversed by one of the trajectories in RI. This talk focuses on the chemical distance of the random interlacements graph in dimensions d \geq 5. In this setting, we will discuss a proof for upper and lower asymptotic bounds on the chemical distance for u << 1. Based on a joint work with Saraí Hernández-Torres, Eviatar B. Procaccia, Balász Ráth and Artëm Sapozhnikov.

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