On sets of zero stationary harmonic measure
Probability
2018-12-24 v4 Mathematical Physics
math.MP
Abstract
In this paper, we prove that any subset with an appropriate sub-linear horizontal growth has a non-zero stationary harmonic measure. On the other hand, we also show any subset with super-linear horizontal growth will have a stationary harmonic measure at every point. This result is fundamental to any future study of stationary DLA. As an application we prove that any possible aggregation process with growth rates proportional to the stationary harmonic measure has non zero measure at all times.
Keywords
Cite
@article{arxiv.1711.01013,
title = {On sets of zero stationary harmonic measure},
author = {Eviatar B. Procaccia and Yuan Zhang},
journal= {arXiv preprint arXiv:1711.01013},
year = {2018}
}
Comments
18 pages, 4 figures