- This event has passed.
Barbara Dembin, ETH Zürich, Switzerland
October 12, 2022 @ 6:00 pm - 7:00 pm UTC+4
Title: “Coalescence of geodesics and the BKS midpoint problem in first-passage percolation.”
Abstract: We consider first-passage percolation on Z^2 with independent and identically distributed weights. Under the assumption that the limit shape has at least 32 extreme points, we prove that geodesics with nearby starting and ending points have significant overlap, coalescing on all but small portions near their endpoints. The statement is quantified, with power-law dependence of the involved quantities on the length of the geodesics.
The result leads to a quantitative resolution of the Benjamini–Kalai–Schramm midpoint problem. It is shown that the probability that a geodesic passes through a given edge is smaller than a power of the distance between that edge and the endpoints of the geodesic. Joint work with Dor Elboim and Ron Peled.