Probability and Mathematical Physics Seminar

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Upper tail large deviations for chemical distance in supercritical percolation

Speaker: Barbara Dembin, ETH Zurich

Location: Warren Weaver Hall 109

Date: Friday, December 9, 2022, 12:05 p.m.

Synopsis:

We consider supercritical bond percolation onZ^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.