A Monotonicity Result for the Range of a Perturbed Random Walk

Lung-Chi Chen () and Rongfeng Sun ()
Additional contact information
Lung-Chi Chen: Fu-Jen Catholic University
Rongfeng Sun: National University of Singapore

Journal of Theoretical Probability, 2014, vol. 27, issue 3, 997-1010

Abstract: Abstract We consider a discrete time simple symmetric random walk on $$\mathbb{Z }^d,\,d\ge 1,$$ where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time $$n\in \mathbb{N }$$ and any deterministic jumps that we insert, the expected number of sites visited by the perturbed random walk up to time $$n$$ is always larger than or equal to that for the unperturbed walk. This intriguing problem arises from the study of a particle among a Poisson system of moving traps with sub-diffusive trap motion. In particular, our result implies a variant of the Pascal principle, which asserts that among all deterministic trajectories the particle can follow, the constant trajectory maximizes the particle’s survival probability up to any time $$t>0.$$

Keywords: Pascal principle; Random walk range; Trapping problem; 60K37; 60K35; 82C22 (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-012-0472-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:27:y:2014:i:3:d:10.1007_s10959-012-0472-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-012-0472-x

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().