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DYNAMICS AND SELF-SIMILARITY IN MIN-DRIVEN CLUSTERING

Abstract:

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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Publication status:
Published

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY More from this journal
Volume:
362
Issue:
12
Pages:
6591-6618
Publication date:
2010-12-01
DOI:
ISSN:
0002-9947
Language:
English
Pubs id:
pubs:103657
UUID:
uuid:a899d93d-203a-4bdf-90f8-dcf432b5095d
Local pid:
pubs:103657
Source identifiers:
103657
Deposit date:
2012-12-19

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