A simplified proof of the relation between scaling exponents in first-passage percolation

Details A simplified proof of the relation between scaling exponents in first-passage percolation A simplified proof of the relation between scaling exponents in first-passage percolation

2011-09-02

arxiv.org/abs/1109.0523v1

Mathematics

Probability

14 pages, 2 figures

Scientific paper

In a recent breakthrough work, Chatterjee proved a long standing conjecture that relates the transversal exponent \xi and the fluctuation exponent \chi in first-passage percolation on Z^d. The purpose of this paper is to introduce a new and intuitive idea that replaces Chatterjee's main argument and gives an alternative proof of this relation. Specifically, we show that under the assumption that exponents (as defined by Chatterjee) exist, one has the relation \chi \leq 2\xi -1. One advantage of our argument is that it does not require a `nearly Gamma' assumption on the edge-weight distribution.

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