Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation

Abstract

We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the increment-stationary variants of the model, and is presented in the context of i.i.d. exponential weights for both zero and near-stationary boundary conditions. A main technical novelty in our approach is a new proof of the left-tail fluctuation upper bound with exponent 3{2 for the last-passage times.

Upper tail bounds for stationary KPZ models

“…For last passage percolation, several moderate and large deviation results are available. Before the results [12,13,14] cited above, which rely on a probabilistic coupling approach as we do, several works deal with tail bounds for the passage time in the moderate deviation regime, and obtain results using integrable probability: [17,23,1]. See also [4,5] for recent, refined large deviation results for the passage time, or equivalently, the Laguerre Unitary Ensemble.…”

“…Assume that c 1 N ≤ max{m, n} ≤ C 1 N for some c 1 , C 1 > 0. Recall the definition of e(a, b, m, n) in (12). Assume a + b = a 3 .…”

“…We refer to this identity as the Rains-EJS identity. It has already found applications to optimal order bounds on the tails and central moments in exponential last passage percolation (the "zero temperature limit" of polymers) [12,13,14].…”