We consider some random subsets of Z^d, d greater or equal to 3, with strong long-range correlation (examples include the trace of simple random walk, random interlacements and level sets of Gaussian free field). We investigate the behavior of the probability that a large body gets disconnected from infinity by this set and derive asymptotic lower and upper bounds that are tight pending on conjectures on the percolations threshold(s) of the vacant set of interlacements and level sets of GFF.
Xinyi Li is an L. E. Dickson instructor at the University of Chicago. He graduated from Peking University and Paris Dauphine University before receiving his Ph.D. degree in mathematics from ETH Zurich. His research interests include random walk, Brownian motion, interlacements and other models for percolation with long-range correlation.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai