# Random walk on half-plane half-comb structure

E. Csáki, Miklós Csörgo, Antónia Földes, Pál Révész

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

We study limiting properties of a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., horizontal lines below the x-axis are removed. We give strong approximations for the components with random time changed Wiener processes. As consequences, limiting distributions and some laws of the iterated logarithm are presented. Finally, a formula is given for the probability that the random walk returns to the origin in 2N steps.

Original language English 29-44 16 Annales Mathematicae et Informaticae 39 Published - 2012

### Fingerprint

Half-plane
Random walk
Strong Approximation
Law of the Iterated Logarithm
Wiener Process
Limiting Distribution
Square Lattice
Horizontal
Limiting
Line

### Keywords

• Anisotropic random walk
• Laws of the iterated logarithm
• Local time
• Strong approximation
• Wiener process

### ASJC Scopus subject areas

• Mathematics(all)
• Computer Science(all)

### Cite this

Csáki, E., Csörgo, M., Földes, A., & Révész, P. (2012). Random walk on half-plane half-comb structure. Annales Mathematicae et Informaticae, 39, 29-44.

Random walk on half-plane half-comb structure. / Csáki, E.; Csörgo, Miklós; Földes, Antónia; Révész, Pál.

In: Annales Mathematicae et Informaticae, Vol. 39, 2012, p. 29-44.

Research output: Contribution to journalArticle

Csáki, E, Csörgo, M, Földes, A & Révész, P 2012, 'Random walk on half-plane half-comb structure', Annales Mathematicae et Informaticae, vol. 39, pp. 29-44.
Csáki, E. ; Csörgo, Miklós ; Földes, Antónia ; Révész, Pál. / Random walk on half-plane half-comb structure. In: Annales Mathematicae et Informaticae. 2012 ; Vol. 39. pp. 29-44.
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