Distances in Hierarchical Percolation

Explore a 44-minute conference talk on hierarchical percolation presented by Lily Reeves from the California Institute of Technology at IPAM's Statistical Mechanics Beyond 2D Workshop. Delve into the toy model of hierarchical percolation and its similarities to percolation on Euclidean lattices, including mean-field behavior in high dimensions and non-mean-field behavior in low dimensions. Discover how the hierarchical lattice enables a renormalization group-style analysis, which is currently challenging for Euclidean lattice percolation. Learn about recent advancements in examining the distribution of chemical distance, extremal distance (effective resistance), and pivotal distance in high dimensions and at the upper-critical dimension, building upon Hutchcroft's work on cluster volumes. Gain insights into this joint research with Tom Hutchcroft, exploring the fascinating world of statistical mechanics and percolation theory.