Chemical distance in high-dimensional percolation

Abstract: Since at least the 1970s, transport properties of critical percolation have been studied in both the physics and mathematics literature. Improving our understanding requires sharp estimates on large-scale geometric properties of critical percolation clusters, including the intrinsic (“chemical’‘) distance and electrical resistance. We show a sharp result for these in high dimensions: the distance and resistance between the origin and a distant vertex converges in distribution when rescaled by a multiple of the square of the Euclidean distance, conditional on these vertices lying in the same cluster.

• Speaker: Jack Hanson (Universität Hamburg)
• Tuesday 03 February 2026, 14:00–15:00
• Venue: MR12.
• Series: Probability; organiser: ww295.