Fluctuation lower bounds in planar random growth models

TL;DR

This paper establishes universal lower bounds on fluctuation growth in three planar random growth models, extending previous results to more general distributions without restrictive assumptions.

Contribution

It proves $\sqrt{ ext{log} n}$ lower bounds on fluctuations and a minimum shape fluctuation exponent of 1/8 for general distributions in planar growth models.

Findings

Lower bounds of $\sqrt{ ext{log} n}$ on growth fluctuations.

Shape fluctuation exponent at least 1/8.

Results hold under minimal distribution assumptions.

Abstract

We prove $\sqrt{\log n}$ lower bounds on the order of growth fluctuations in three planar growth models (first-passage percolation, last-passage percolation, and directed polymers) under no assumptions on the distribution of vertex or edge weights other than the minimum conditions required for avoiding pathologies. Such bounds were previously known only for certain restrictive classes of distributions.In addition, the first-passage shape fluctuation exponent is shown to be at least $1/8$, extending previous results to more general distributions.