Subdiffusive concentration in first-passage percolation

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We prove exponential concentration in i.i.d. first-passage percolation in Zᵈ for all d ≥ 2 and general edge-weights (tₑ). Precisely, under an exponential moment assumption E eαᵗᵉ< ∞ for some α>0) on the edge-weight distribution, we prove the inequality P(|T(0,x)-E T(0,x)| ≥ λ√|x|/log |x|) ≤ ce⁻ᶜ' λ, |x|>1 for the point-to-point passage time T(0,x). Under a weaker assumption E tₑ²(tₑ)+< ∞ we show a corresponding inequality for the lower-tail of the distribution of T(0,x). These results extend work of Benaim-Rossignol to general distributions.