Probability Seminar: Balazs Rath
- Date: 01/30/2013
- Time: 15:00
University of British Columbia
On chemical distances and shape theorems in percolation models with long-range correlations
We provide general conditions on a one parameter family of random infinite subsets of Z^d to contain a unique infinite connected component for which the chemical distances are comparable to the Euclidean distances, focusing primarily on models with long-range correlations. We also prove a shape theorem for balls in the chemical distance under such conditions. Our general statements give novel results about the structure of the infinite connected component of the vacant set of random interlacements and the level sets of the Gaussian free field. As a corollary, we obtain new results about the (chemical) diameter of the largest connected component in the complement of the trace of the random walk on the torus. Joint work with Alexander Drewitz and Artem Sapozhnikov.
Location: EBS 2012