Asymptotics of the odometer function for the internal Diffusion Limited Aggregation model

TL;DR

This paper provides precise asymptotic analysis of the odometer function in the internal Diffusion Limited Aggregation model, enhancing understanding of its behavior and offering a new proof of a key time-scale result.

Contribution

It offers detailed asymptotics for the odometer function and presents an alternative proof for a significant time-scale result in IDLA.

Findings

Asymptotic formulas for the odometer function derived

New proof of Lawler, Bramson, and Griffeath's time-scale result

Improved understanding of IDLA growth dynamics

Abstract

We present precise asymptotics of the odometer function for the internal Diffusion Limited Aggregation model. These results provide a better understanding of this function whose importance was demonstrated by Levine and Peres. We derive a different proof of a time-scale result by Lawler, Bramson and Griffeath.