Probability Seminar

Date: November 20, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Jiayan Ye, TAMU

Title: Continuity of cheeger constant in super-critical percolation

Abstract: Abstract: We consider the super-critical bond percolation on $Z^d$ with $d \geq 3$ and $p > p_c(Z^d)$. In particular, we study the subgraphs of $C_{\infty} \cap [-n, n]^d$ with minimal cheeger constant, where $C_{\infty}$ is the unique infinite open cluster on $Z^d$. Recently, Gold proved that the subgraphs converge to a deterministic shape almost surely. We prove that this deterministic shape is Hausdrorff - continuous in the percolation parameter $p$. This is joint work with Eviatar Procaccia.