The Limiting Shape for Drifted Internal Diffusion Limited Aggregation is a True Heat Ball
Probability
2013-02-19 v2 Analysis of PDEs
Abstract
We build the iDLA cluster using drifted random walks, and study the limiting shapes they exhibit, with the help of sandpile models. For constant drift, the normalised cluster converges to a canonical shape S, which can be termed a true heat ball, in that it gives rise to a mean value property for caloric functions. The existence and boundedness of such a shape answers a natural yet open question in PDE theory.
Cite
@article{arxiv.1202.2032,
title = {The Limiting Shape for Drifted Internal Diffusion Limited Aggregation is a True Heat Ball},
author = {Cyrille Lucas},
journal= {arXiv preprint arXiv:1202.2032},
year = {2013}
}
Comments
Corrected a number a typos and cleared up a few points in the proofs