Sublinear variance for directed last-passage percolation

TL;DR

This paper proves that directed last-passage percolation with Gaussian weights exhibits sublinear variance, supporting the conjecture that such models display superdiffusivity and related properties.

Contribution

It establishes sublinear variance for directed last-passage percolation with Gaussian weights and extends results to other vertex weight distributions and directed polymers.

Findings

Sublinear variance proven for Gaussian vertex weights

Results extended to other weight distributions

Connections made to directed polymers in random environments

Abstract

A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear variance property. We also consider other vertex weight distributions. Corresponding results are obtained for the ground state of the `directed polymers in a random environment' model.