Modul: MAT971 Seminar über stochastische Prozesse

## Upper tail large deviations for chemical distance in supercritical percolation

Talk by Dr. Barbara Dembin

**Date:** 15.03.23 **Time:** 17.15 - 18.45 **Room:** Y27H12

We consider supercritical bond percolation on Z^d and study the chemical distance, i.e., the graph distance on the infinite cluster. It is well-known that there exists a deterministic constant μ(x) such that the chemical distance D(0,nx) between two connected points 0 and nx grows like nμ(x). We prove the existence of the rate function for the upper tail large deviation event {D(0,nx)>nμ(x)(1+ϵ),0↔nx} for d>=3.

Joint work with Shuta Nakajima.