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Random Walks on Comb-Type Subsets of \(\mathbb {Z}^2\)

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Abstract

We study the path behavior of the simple symmetric walk on some comb-type subsets of \({{\mathbb {Z}}}^2\) which are obtained from \({{\mathbb {Z}}}^2\) by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation results and discuss their consequences.

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Acknowledgements

The authors are indebted to Miklós Csörgő and Pál Révész for their inspiration and careful reading of our manuscript that greatly improved our presentation. We also would like to thank our referee for his/her insightful suggestions which made our presentation much nicer.

Funding

Funding was provided by Research Foundation of The City University of New York (Grant No: 61520-0049).

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O.B. 127, 1364, Hungary

    Endre Csáki

  2. Department of Mathematics, College of Staten Island, CUNY, 2800 Victory Blvd., Staten Island, New York, 10314, USA

    Antónia Földes

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  1. Endre Csáki
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  2. Antónia Földes
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Correspondence to Antónia Földes.

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A. Földes: Research supported by a PSC CUNY Grant, No. 61520-0049.

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Csáki, E., Földes, A. Random Walks on Comb-Type Subsets of \(\mathbb {Z}^2\). J Theor Probab 33, 2233–2257 (2020). https://doi.org/10.1007/s10959-019-00938-5

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  • DOI: https://doi.org/10.1007/s10959-019-00938-5

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