UZH-Logo

Maintenance Infos

The drift of a one-dimensional self-repellent random walk with bounded increments


König, W (1994). The drift of a one-dimensional self-repellent random walk with bounded increments. Probability Theory and Related Fields, 100(4):513-544.

Abstract

Consider a one-dimensional walk (Sk)k having steps of bounded size, and weight the probability of the path with some factor 1−α∈(0,1) for every single self-intersection up to time n. We prove that Sn/n converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as α tends to 0 and, as α tends to 1, to the self-avoiding walk's drift which was introduced in an earlier paper of ours [Probab. Theory Related Fields 96 (1993), no. 4, 521--543]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.

Consider a one-dimensional walk (Sk)k having steps of bounded size, and weight the probability of the path with some factor 1−α∈(0,1) for every single self-intersection up to time n. We prove that Sn/n converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as α tends to 0 and, as α tends to 1, to the self-avoiding walk's drift which was introduced in an earlier paper of ours [Probab. Theory Related Fields 96 (1993), no. 4, 521--543]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.

Citations

5 citations in Web of Science®
8 citations in Scopus®
Google Scholar™

Altmetrics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1994
Deposited On:29 Nov 2010 16:29
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0178-8051
Publisher DOI:https://doi.org/10.1007/BF01268992
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1305785
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0810.60095

Download

Full text not available from this repository.View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations