Dynamics and self-similarity in min-driven clustering
Adaptation and Self-Organizing Systems
2013-05-16 v1
Abstract
We study a mean-field model for a clustering process that may be described informally as follows. At each step a random integer is chosen with probability , and the smallest cluster merges with randomly chosen clusters. We prove that the model determines a continuous dynamical system on the space of probability measures supported in , and we establish necessary and sufficient conditions for approach to self-similar form. We also characterize eternal solutions for this model via a Levy-Khintchine formula. The analysis is based on an explicit solution formula discovered by Gallay and Mielke, extended using a careful choice of time scale.
Cite
@article{arxiv.0807.4473,
title = {Dynamics and self-similarity in min-driven clustering},
author = {Govind Menon and Barbara Niethammer and Robert L. Pego},
journal= {arXiv preprint arXiv:0807.4473},
year = {2013}
}