A Large-Deviation Upperbound on Directed Last-Passage Percolation Growth Rate Based on Entropy of Direction Vector

TL;DR

This paper introduces a large-deviation upper bound for the growth rate in directed last-passage percolation, utilizing the entropy of the direction vector to quantify the probability of atypical growth behaviors.

Contribution

It presents a novel large-deviation upper bound for LPP growth rate based on the entropy of the direction vector, offering new insights into the probabilistic structure of LPP.

Findings

Provides a new upper bound on LPP growth rate

Uses entropy of direction vector for probabilistic analysis

Enhances understanding of large deviations in LPP

Abstract

This short note provides a large-deviation-based upper bound on the growth rate of directed last passage percolation (LPP) using the entropy of the normalized direction vector.