Tightness of Fluctuations of First Passage Percolation on Some Large Graphs

Itai Benjamini; Ofer Zeitouni

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Tightness of Fluctuations of First Passage Percolation on Some Large Graphs

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arxiv 1010.1412 v2 pith:TDONFNJH submitted 2010-10-07 math.PR math.MG

Itai Benjamini , Ofer Zeitouni This is my paper · ORCID

classification math.PRmath.MG

keywords graphsclassfirstgraphpassagepercolationtightnessaround

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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.

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