# Coupling Derivation of Optimal-Order Central Moment Bounds in Exponential Last-Passage Percolation

## TL;DR

This paper introduces new methods to analyze statistical properties in a mathematical model of random growth.

## Contribution

A novel proof technique for deriving central moment bounds in last-passage percolation with exponential weights.

## Key findings

- A new proof of the left-tail fluctuation upper bound with exponent 3/2 for last-passage times.
- Optimal-order central moment bounds are derived for exponential weights under zero and near-stationary boundary conditions.
- The technique uses couplings with increment-stationary variants of the model.

## 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.