Sublinear variance in first-passage percolation for general distributions

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.

32 pages. We added a proof sketch and fixed the proof of Theorem 2.3 and the bound on term (6.18)

References in corpus (3)

• First passage percolation and competition models
• Percolation since Saint-Flour
• Subgaussian concentration and rates of convergence in directed polymers

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• Localization and free energy asymptotics in disordered statistical mechanics and random growth models
• Sublinear variance in Euclidean first-passage percolation
• Transversal fluctuations for a first passage percolation model
• Divergence of non-random fluctuation in First Passage Percolation
• Passage time of the frog model has a sublinear variance