Stochastic domination for the last passage percolation model

TL;DR

This paper introduces a stochastic domination approach for the last passage percolation model on the positive integer lattice, providing new insights into the structure of subtrees within this probabilistic framework.

Contribution

It presents a novel stochastic domination technique for comparing subtrees in the last passage percolation model, advancing theoretical understanding of its probabilistic structure.

Findings

Established a stochastic domination relation between subtrees

Provided new bounds for last passage times

Enhanced understanding of the model's probabilistic structure

Abstract

A competition model on $\mathbb{Z}_+^{2}$ governed by directed last passage percolation is considered. A stochastic domination argument between subtrees of the last passage percolation is put forward.