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.
Keywords
Cite
@article{arxiv.2204.06613,
title = {Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation},
author = {Elnur Emrah and Nicos Georgiou and Janosch Ortmann},
journal= {arXiv preprint arXiv:2204.06613},
year = {2025}
}
Comments
48 pages, 1 figure. Improved exposition. The first two sections rewritten. The results and the proofs are the same but their presentation has changed. Previous Propositions 4.1, 4.5 and B.1 are now Theorems 2.6, 2.3 and 2.7, respectively. Omitted Appendix C and some minor extensions/variations of the results. Shortened the bibliography but also added some new references