Electronic Journal of Probability

Positively and negatively excited random walks on integers, with branching processes

Elena Kosygina and Martin Zerner

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We consider excited random walks on the integers with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right. We extend the criteria for recurrence and transience by M. Zerner and for positivity of speed by A.-L. Basdevant and A. Singh to this case and also prove an annealed central limit theorem. The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.

Article information

Electron. J. Probab., Volume 13 (2008), paper no. 64, 1952-1979.

Accepted: 6 November 2008
First available in Project Euclid: 1 June 2016

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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]
Secondary: 60K37: Processes in random environments 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Central limit theorem excited random walk law of large numbers positive and negative cookies recurrence renewal structure transience

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Kosygina, Elena; Zerner, Martin. Positively and negatively excited random walks on integers, with branching processes. Electron. J. Probab. 13 (2008), paper no. 64, 1952--1979. doi:10.1214/EJP.v13-572. https://projecteuclid.org/euclid.ejp/1464819137

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