Tightness of Fluctuations of First Passage Percolation on Some Large Graphs

2010/10/07 by Itaï Benjamini, Benjamini, Itai, Ofer Zeitouni +1 · 3 citations
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Metric Geometry (math.MG) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1010.1412

openalex publication_date 2010/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The theorem of Dekking and Host regarding tightness around the mean of first passage percolation on the binary tree, from the root to a boundary of a ball, is generalized to a class of graphs which includes all lattices in hyperbolic spaces and the lamplighter graph over N. This class of graphs is closed under product with any bounded degree graph. Few open problems and conjectures are gathered at the end.

Cited by

• First-passage percolation, non-positive curvature, and radial maps
• Random Trees in Hyperbolic FPP
• Sublinear Morse Geodesics and First Passage Percolation

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