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A temporal perspective on the rate of convergence in first-passage percolation under a moment condition. (English) Zbl 1478.60251

Summary: We study the rate of convergence in the celebrated Shape Theorem in first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are presented from a temporal perspective and complement previous work by the same author, in which the rate of convergence was studied from the standard spatial perspective.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F15 Strong limit theorems