Point-to-point distance in first passage percolation on (tree) x Z
Probability
2018-06-20 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1310.4018,
title = {Point-to-point distance in first passage percolation on (tree) x Z},
author = {Itai Benjamini and Pascal Maillard},
journal= {arXiv preprint arXiv:1310.4018},
year = {2018}
}
Comments
4 pages, published version