Border aggregation model
Probability
2017-02-06 v1
Abstract
Start with a graph with a subset of vertices called {\it the border}. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at which point it joins this subset thus increasing the border by one point. Then a new particle is released from the origin and the process repeats until the origin becomes a part of the border itself. We are interested in the total number of particles to be released by this final moment. We show that this model covers OK Corral model as well as the erosion model, and obtain distributions and bounds for in cases where the graph is star graph, regular tree, and a dimensional lattice.
Cite
@article{arxiv.1702.01077,
title = {Border aggregation model},
author = {Debleena Thacker and Stanislav Volkov},
journal= {arXiv preprint arXiv:1702.01077},
year = {2017}
}