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research article
The Range of a Random Walk on a Comb
The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of v, each with probability 1/d(v), where d(v) denotes the degree of v. We answer a question of Csaki, Csorgo, Foldes, Revesz, and Tusnady by showing that the expected number of vertices visited by a random walk on the comb after n steps is (1/2 root 2 pi + o(1)) root n log n. This contradicts a claim of Weiss and Havlin.
Type
research article
Web of Science ID
WOS:000325472100005
Authors
Publication date
2013
Publisher
Published in
Volume
20
Issue
3
Start page
P59
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
December 9, 2013
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