Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights

2025/02/02 by Tom Alberts, Alberts, Tom, Riddhipratim Basu +5 · 1 citation
Mathematics · #60K35 #60K37 #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2502.00942

openalex publication_date 2025/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation limit for the midpoint transversal fluctuations in a general last-passage percolation (LPP) model with mild assumption on the i.i.d. weights. The rate function is expressed in terms of the right tail large deviation rate function of the last-passage value and the shape function. When the weights are chosen to be i.i.d. exponential random variables, our result verifies a conjecture communicated to us by Liu [Liu'22], showing the asymptotic probability of the geodesic from (0,0) to (n,n) following the corner path (0,0) → (n,0) → (n,n) is (4/e²)^n+o(n).

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