Surviving ends in Bernoulli percolation on graphs roughly isometric to a tree

Kainan Xiang and Lang Zou

Statistics & Probability Letters, 2022, vol. 184, issue C

Abstract: Let G be an infinite locally-finite connected graph roughly isometric to a tree, and o a fixed vertex of G. Given any p∈(0,1). Then under a mild condition, the number of surviving ends under Bernoulli-p bond percolation ω on G a.s. either is 0 or has the cardinality of the continuum; which generalizes Proposition 5.27 in Lyons and Peres (2016) from a viewpoint of rough isometry. Here a surviving end is an end of G induced by a surviving ray from o in the ω.

Keywords: Percolation; Surviving end; Rough isometry; Tree (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109378

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