# The range of a random walk on a comb

János Pach, G. Tardos

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

The graph obtained from the integer grid ℤ×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, Csörgo{double acute}, Földes, Révész, and Tusnády by showing that the expected number of vertices visited by a random walk on the comb after n steps is. This contradicts a claim of Weiss and Havlin.

Original language English Electronic Journal of Combinatorics 20 3 Published - Oct 7 2013

### Fingerprint

Random walk
Graph in graph theory
Acute
Range of data
Horizontal
Denote
Grid
Integer
Vertex of a graph

• Random walk

### ASJC Scopus subject areas

• Geometry and Topology
• Theoretical Computer Science
• Computational Theory and Mathematics

### Cite this

The range of a random walk on a comb. / Pach, János; Tardos, G.

In: Electronic Journal of Combinatorics, Vol. 20, No. 3, 07.10.2013.

Research output: Contribution to journalArticle

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