Probability Seminar

Title: Planar percolation and Benjamini-Schramm conjecture
Speaker: Zhongyang Li
Speaker Info: University of Connecticut
Brief Description:
Special Note:

I will show that for a non-amenable, locally finite, connected, transitive, planar graph with one end, any automorphism invariant site percolation on the graph does not have exactly 1 infinite 1-cluster and exactly 1 infinite 0-cluster a.s. If we further assume that the site percolation is insertion-tolerant and a.s.~there exists a unique infinite 0-cluster, then a.s.~there are no infinite 1-clusters. I will also discuss how to apply these results to solve two conjectures of Benjamini and Schramm in 1996.
Date: Wednesday, February 03, 2021
Time: 4:00PM
Where: https://northwestern.zoom.us/j/907400031
Contact Person: Antonio Auffinger
Contact email: tuca@northwestern.edu
Contact Phone:
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