• Corpus ID: 231648205

# A variational formula for large deviations in First-passage percolation under tail estimates

```@inproceedings{Cosco2021AVF,
title={A variational formula for large deviations in First-passage percolation under tail estimates},
author={Cl{\'e}ment Cosco and Shuta Nakajima},
year={2021}
}```
• Published 20 January 2021
• Mathematics
Consider first passage percolation with identical and independent weight distributions and first passage time T. In this paper, we study the upper tail large deviations P(T(0, nx) > n(μ + ξ)), for ξ > 0 and x 6= 0 with a time constant μ and a dimension d, for weights that satisfy a tail assumption β1 exp (−αt) ≤ P(τe > t) ≤ β2 exp (−αt). When r ≤ 1 (this includes the wellknown Eden growth model), we show that the upper tail large deviation decays as exp (−(2dξ + o(1))n). When 1 < r ≤ d, we find…

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