Conservative random walk*
(2022) In Electronic Journal of Probability 27.- Abstract
Recently, in [11], the “coin-turning walk” was introduced on Z. It is a non-Markovian process where the steps form a (possibly) time-inhomogeneous Markov chain. In this article, we follow up the investigation by introducing analogous processes in Zd, d ≥ 2: at time n the direction of the process is “updated” with probability pn; otherwise the next step repeats the previous one. We study some of the fundamental properties of these walks, such as transience/recurrence and scaling limits. Our results complement previous ones in the literature about “correlated” (or “Newtonian”) and “persistent” random walks.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/9bae54f6-4044-466e-87b9-d87d0a61e13b
- author
- Engländer, János and Volkov, Stanislav LU
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- coin-turning, conservative random walk, cooling dynamics, correlated random walk, heating dynamics, invariance principle, Newtonian random walk, persistent random walk, random walk, recurrence, scaling limits, time-inhomogeneous Markov-processes, transience
- in
- Electronic Journal of Probability
- volume
- 27
- article number
- 138
- publisher
- UNIV WASHINGTON, DEPT MATHEMATICS
- external identifiers
-
- scopus:85139963133
- ISSN
- 1083-6489
- DOI
- 10.1214/22-EJP863
- language
- English
- LU publication?
- yes
- id
- 9bae54f6-4044-466e-87b9-d87d0a61e13b
- date added to LUP
- 2022-12-19 15:28:10
- date last changed
- 2022-12-19 15:28:10
@article{9bae54f6-4044-466e-87b9-d87d0a61e13b, abstract = {{<p>Recently, in [11], the “coin-turning walk” was introduced on Z. It is a non-Markovian process where the steps form a (possibly) time-inhomogeneous Markov chain. In this article, we follow up the investigation by introducing analogous processes in Z<sup>d</sup>, d ≥ 2: at time n the direction of the process is “updated” with probability p<sub>n</sub>; otherwise the next step repeats the previous one. We study some of the fundamental properties of these walks, such as transience/recurrence and scaling limits. Our results complement previous ones in the literature about “correlated” (or “Newtonian”) and “persistent” random walks.</p>}}, author = {{Engländer, János and Volkov, Stanislav}}, issn = {{1083-6489}}, keywords = {{coin-turning; conservative random walk; cooling dynamics; correlated random walk; heating dynamics; invariance principle; Newtonian random walk; persistent random walk; random walk; recurrence; scaling limits; time-inhomogeneous Markov-processes; transience}}, language = {{eng}}, publisher = {{UNIV WASHINGTON, DEPT MATHEMATICS}}, series = {{Electronic Journal of Probability}}, title = {{Conservative random walk<sup>*</sup>}}, url = {{http://dx.doi.org/10.1214/22-EJP863}}, doi = {{10.1214/22-EJP863}}, volume = {{27}}, year = {{2022}}, }