Abstract
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 Csáki, Csörgö, Földes, Révész, and Tusnády by showing that the expected number of vertices visited by a random walk on the comb after n steps is (1/(2\sqrt{2π})+o(1))\sqrt n\log n. This contradicts a claim of Weiss and Havlin.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.