Point-to-point distance in first passage percolation on (tree) x Z

Itai Benjamini; Pascal Maillard

doi:10.1007/978-3-319-09477-9

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arXiv · 1310.4018

Point-to-point distance in first passage percolation on (tree) x Z

Itai Benjamini·Pascal Maillard

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Abstract

We consider first passage percolation (FPP) on T_d x Z, where T_d is the d-regular tree (d>=3). It is shown that for a fixed vertex v in the tree, the fluctuation of the distance in the FPP metric between the points (v,0) and (v,n) is of the order of at most log n. We conjecture that the real fluctuations are of order 1 and explain why.

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Itai Benjamini, Pascal Maillard. 2013-10-15. Point-to-point distance in first passage percolation on (tree) x Z. https://doi.org/10.1007/978-3-319-09477-9

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