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.
"A temporal perspective on the rate of convergence in first-passage percolation under a moment condition." Braz. J. Probab. Stat. 33 (2) 397 - 401, May 2019. https://doi.org/10.1214/18-BJPS394