Tsukuba Journal of Mathematics

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

Kazuki Okamura

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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

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

First available in Project Euclid: 13 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

self-interacting random walk range of random walk


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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