Two-Dimensional Rademacher Walk
Bhattacharya, Satyaki LU and Volkov, Stanislav LU
(2026)
In Journal of Theoretical Probability
39(2).
- Abstract
We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (ALEA Lat. Am. J. Probab. Math. Stat. 20(1):33–51, 2023) to Z2 (for d≥3, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Engländer and Volkov (Coin Turning, Random Walks and Inhomogeneous Markov Chains, World Scientific and Volkov, Singapore, 2025)). This walk is defined as the sum of a sequence of independent steps, where each step goes in one of the four possible directions with equal probability, and the size of the nth step is an where {an} is a given sequence of positive integers. We establish some general conditions under which the walk is recurrent or transient.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2c331868-b9f1-4368-bc1e-30de9e3bcd5d
- author
- Bhattacharya, Satyaki
LU
and Volkov, Stanislav
LU
- organization
- publishing date
- 2026
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Non-homogeneous Markov chains, Rademacher distribution, Recurrence, Transience
- in
- Journal of Theoretical Probability
- volume
- 39
- issue
- 2
- article number
- 40
- publisher
- Springer
- external identifiers
-
- scopus:105035096738
- ISSN
- 0894-9840
- DOI
- 10.1007/s10959-026-01497-2
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © The Author(s) 2026.
- id
- 2c331868-b9f1-4368-bc1e-30de9e3bcd5d
- date added to LUP
- 2026-05-26 13:39:49
- date last changed
- 2026-05-26 13:39:49
@article{2c331868-b9f1-4368-bc1e-30de9e3bcd5d,
abstract = {{<p>We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (ALEA Lat. Am. J. Probab. Math. Stat. 20(1):33–51, 2023) to Z2 (for d≥3, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Engländer and Volkov (Coin Turning, Random Walks and Inhomogeneous Markov Chains, World Scientific and Volkov, Singapore, 2025)). This walk is defined as the sum of a sequence of independent steps, where each step goes in one of the four possible directions with equal probability, and the size of the nth step is an where {an} is a given sequence of positive integers. We establish some general conditions under which the walk is recurrent or transient.</p>}},
author = {{Bhattacharya, Satyaki and Volkov, Stanislav}},
issn = {{0894-9840}},
keywords = {{Non-homogeneous Markov chains; Rademacher distribution; Recurrence; Transience}},
language = {{eng}},
number = {{2}},
publisher = {{Springer}},
series = {{Journal of Theoretical Probability}},
title = {{Two-Dimensional Rademacher Walk}},
url = {{http://dx.doi.org/10.1007/s10959-026-01497-2}},
doi = {{10.1007/s10959-026-01497-2}},
volume = {{39}},
year = {{2026}},
}