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arXiv · 1306.1197

Sublinear variance in first-passage percolation for general distributions

Michael Damron·Jack Hanson·Philippe Sosoe
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Abstract

We prove that the variance of the passage time from the origin to a point x in first-passage percolation on Z^d is sublinear in the distance to x when d \geq 2, obeying the bound Cx/(log x), under minimal assumptions on the edge-weight distribution. The proof applies equally to absolutely continuous, discrete and singular continuous distributions and mixtures thereof, and requires only 2+log moments. The main result extends work of Benjamini-Kalai-Schramm and Benaim-Rossignol.

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Michael Damron, Jack Hanson, Philippe Sosoe. 2013-06-05. Sublinear variance in first-passage percolation for general distributions. https://doi.org/10.1007/s00440-014-0591-7

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