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arXiv · 1804.05718

Fluctuations in first-passage percolation

Philippe Sosoe
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Abstract

We present a survey of techniques to obtain upper bounds for the variance of the passage time in first-passage percolation. The methods discussed are a combination of tools from the theory of concentration of measure, some of which we briefly review. These are combined with variations on an idea of Benjamini-Kalai-Schramm to obtain a logarithmic improvement over the linear bound implied by the Efron-Stein/Poincare inequality, for general edge-weight distributions.

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Philippe Sosoe. 2018-04-16. Fluctuations in first-passage percolation. https://arxiv.org/abs/1804.05718

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