Tsukuba Journal of Mathematics

On the range of self-interacting random walks on an integer interval

Kazuki Okamura

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Abstract

We consider the range of a one-parameter family of selfinteracting walks on the integers up to the time of exit from an interval. We derive the weak convergence of an appropriately scaled range. We show that the distribution functions of the limits of the scaled range satisfy a certain class of de Rham's functional equations. We examine the regularity of the limits.

Article information

Source
Tsukuba J. Math., Volume 38, Number 1 (2014), 123-135.

Dates
First available in Project Euclid: 13 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1407938675

Digital Object Identifier
doi:10.21099/tkbjm/1407938675

Mathematical Reviews number (MathSciNet)
MR3261916

Zentralblatt MATH identifier
1305.60104

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
self-interacting random walk range of random walk

Citation

Okamura, Kazuki. On the range of self-interacting random walks on an integer interval. Tsukuba J. Math. 38 (2014), no. 1, 123--135. doi:10.21099/tkbjm/1407938675. https://projecteuclid.org/euclid.tkbjm/1407938675


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