# 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.

## Key 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.