DYNAMICS AND SELF-SIMILARITY IN MIN-DRIVEN CLUSTERING

Journal article

We study a mean-field model for a clustering process that may be described informally as follows. At each step a random integer k is chosen with probability pk, and the smallest cluster merges with k randomly hosen clusters. We prove that the model determines a continuous dynamical system on the space of probability measures supported in (0,∞), and we establish necessary and sufficient conditions for the approach to self-similar form. We also characterize eternal solutions for this model via ...

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Authors: Menon, G; Niethammer, B; Pego, R

• Publication status: Published
• Journal: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• Volume: 362
• Issue: 12
• Pages: 6591-6618
• Publication date: 2010-12-01
• DOI: 10.1090/S0002-9947-2010-05085-8
• ISSN: 0002-9947
• Language: English