Journal article icon

Journal article

Vertex-reinforced random walk on Z eventually gets stuck on five points

Abstract:

Vertex-reinforced random walk (VRRW), defined by Pemantle in 1988, is a random process that takes values in the vertex set of a graph G, which is more likely to visit vertices it has visited before. Pemantle and Volkov considered the case when the underlying graph is the one-dimensional integer lattice ℤ. They proved that the range is almost surely finite and that with positive probability the range contains exactly five points. They conjectured that this second event holds with probability 1...

Expand abstract
Publication status:
Published

Actions


Access Document


Publisher copy:
10.1214/009117907000000694

Authors


More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
ANNALS OF PROBABILITY
Volume:
32
Issue:
3B
Pages:
2650-2701
Publication date:
2004-07-05
DOI:
ISSN:
0091-1798
URN:
uuid:bd38fbfc-6073-4477-85c6-6f8237fbb635
Source identifiers:
13696
Local pid:
pubs:13696

Terms of use


Metrics


Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP