On the chemical distance in critical percolation II

2016/01/14 by Michael Damron, Damron, Michael, Jack Hanson +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1601.03464

openalex publication_date 2016/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue our study of the chemical (graph) distance inside large critical percolation clusters in dimension two. We prove new estimates, which involve the three-arm probability, for the point-to-surface and point-to-point distances. We show that the point-to-point distance in ℤ² between two points in the same critical percolation cluster has infinite second moment. We also give quantitative versions of our previous results comparing the length of the shortest crossing to that of the lowest crossing of a box.

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