Random walk on half-plane half-comb structure

Endre Csáki, Miklós Csörgo, Antónia Földes, Pál Révész

Research output: Contribution to journalArticle

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)29-44
Number of pages16
JournalAnnales Mathematicae et Informaticae
Publication statusPublished - Jul 26 2012



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

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(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.