Abstract
AbstractWe consider first passage percolation (FPP) on \(\mathbb{T}_{d} \times G\), where \(\mathbb{T}_{d}\) is the d-regular tree (d ≥ 3) and G is a graph containing an infinite ray 0, 1, 2, …. 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 logn. We conjecture that the real fluctuations are of order 1 and explain why.KeywordsFirst-passage Percolation (FPP)Real FluctuationsBranching Random WalkPath LooksHigh-dimensional Euclidean SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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