Quasi-Isometric Nonequivalence for Random Subsets in Products of Trees

Explore quasi-isometric embeddings from random Bernoulli percolation samples on products of two regular trees in this 48-minute conference talk by Tianyi Zheng from the University of California, San Diego, presented at IPAM's New Interactions Between Probability and Geometry Workshop. Examine rigidity properties that extend quasi-isometric rigidity of higher rank non-uniform lattices, and discover how two independent samples are almost surely not quasi-isometric equivalent. Learn about the confirmation of this phenomenon in higher-rank settings, as originally conjectured by Abert, through joint research with Zhiqiang Li and Ranfeng Yu. Gain insights into the intersection of probability theory and geometric group theory through this advanced mathematical presentation that bridges random processes on tree products with quasi-isometric geometry.