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DYNAMICS OF VERTEX-REINFORCED RANDOM WALKS

Abstract:

We generalize a result from Volkov [Ann. Probab. 29 (2001) 66-91] and prove that, on a large class of locally finite connected graphs of bounded degree (G, ~) and symmetric reinforcement matrices a = (a i,j ) i,j∈G, the vertex-reinforced random walk (VRRW) eventually localizes with positive probability on subsets which consist of a complete d-partite subgraph with possible loops plus its outer boundary. We first show that, in general, any stable equilibrium of a linear symmetric replicator dy...

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Publication status:
Published

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Publisher copy:
10.1214/10-AOP609

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Institution:
University of Oxford
Department:
Oxford, SSD, Divisional Administration, Oxford-Man Institute
Role:
Author
Journal:
ANNALS OF PROBABILITY
Volume:
39
Issue:
6
Pages:
2178-2223
Publication date:
2011-11-05
DOI:
ISSN:
0091-1798
URN:
uuid:7f3d9c6b-b463-4bcd-b201-b2ee62a7879f
Source identifiers:
213449
Local pid:
pubs:213449

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