Recorded 27 January 2026. Tianyi Zheng of the University of California, San Diego, presents "Quasi-isometric nonequivalence for random subsets in products of trees" at IPAM's New Interactions Between Probability and Geometry Workshop. Abstract: We study quasi-isometric embeddings from a random Bernoulli percolation sample on the product of two regular trees into the product itself, and show some rigidity properties that can be seen as an extension of quasi-isometric rigidity of higher rank non-uniform lattices. We also prove that two independent samples are almost surely not quasi-isometric equivalent, thus confirming that such a phenomenon occurs in the higher-rank setting, as conjectured by Abert. Joint work with Zhiqiang Li and Ranfeng Yu. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/new-interactions-between-probability-and-geometry/?tab=overview