### 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 |
---|---|

Journal | Electronic Journal of Combinatorics |

Volume | 20 |

Issue number | 3 |

Publication status | Published - Oct 7 2013 |

### Fingerprint

### Keywords

- Random walk

### ASJC Scopus subject areas

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

### Cite this

*Electronic Journal of Combinatorics*,

*20*(3).

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

Research output: Contribution to journal › Article

*Electronic Journal of Combinatorics*, vol. 20, no. 3.

}

TY - JOUR

T1 - The range of a random walk on a comb

AU - Pach, János

AU - Tardos, G.

PY - 2013/10/7

Y1 - 2013/10/7

N2 - 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.

AB - 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.

KW - Random walk

UR - http://www.scopus.com/inward/record.url?scp=84885463452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885463452&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84885463452

VL - 20

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 3

ER -