Planar Site Percolation via Tree Embeddings

Explore a lecture on planar site percolation through tree embeddings presented by Zhongyang Li from the University of Connecticut at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into the proof of a conjecture by Benjamini and Schramm from 1996, demonstrating that for infinite, connected planar graphs with minimal vertex degree of at least 7, i.i.d. Bernoulli(p) site percolation almost surely results in infinitely many infinite 1-clusters within a specific probability interval. Discover the novel construction of embedded trees on such graphs, which forms the basis of the proof. Gain insights into the properties of site percolation on planar graphs and their implications for statistical mechanics and discrete geometry.