Moderate deviations in first-passage percolation for bounded weights
Abstract
We investigate the moderate and large deviations in first-passage percolation (FPP) with bounded weights on Zd for d ≥ 2. Write T(x, y) for the first-passage time and denote by μ(u) the time constant in direction u. In this paper, we establish that, if one assumes that the sublinear error term T(0, Nu) − Nμ(u) is of order Nχ, then under some unverified (but widely believed) assumptions, for χ < a < 1, P(T(0,Nu)>Nμ(u)+Na)=exp(−Nd(1+o(1))1−χ(a−χ)) and P(T(0,Nu)
Fields of Study & Subjects
Random Matrices and Applications
Stochastic processes and statistical mechanics
Bayesian Methods and Mixture Models
Publication details
- Journal / source
- Journal of Mathematical Physics
- Volume
- 67
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN