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Conservative random walk*

Engländer, János and Volkov, Stanislav LU orcid (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.

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author
and
organization
publishing date
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}},
}