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Attracting edge and strongly edge reinforced walks

Abstract:

The goal is to show that an edge-reinforced random, walk on a graph of bounded degree, with reinforcement weight function W taken from a general class of reciprocally summable reinforcement weight functions, traverses a random attracting edge at all large times. The statement of the main theorem is very close to settling a conjecture of Sellke [Technical Report 94-26 (1994) Purdue Univ.]. An important corollary of this main result says that if W is reciprocally summable and nondecreasing, the...

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Publication status:
Published

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Publisher copy:
10.1214/009117906000001097

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Institution:
University of Oxford
Department:
Oxford, SSD, Divisional Administration, Oxford-Man Institute
Journal:
ANNALS OF PROBABILITY
Volume:
35
Issue:
5
Pages:
1783-1806
Publication date:
2007-09-05
DOI:
ISSN:
0091-1798
URN:
uuid:8b82583c-adb3-4060-9249-d407b66bcc55
Source identifiers:
29534
Local pid:
pubs:29534

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