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

Elena Kosygina (Baruch College and the CUNY Graduate Center)
Martin P.W. Zerner (University of Tuebingen)

Abstract


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.

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Pages: 1952-1979

Publication Date: November 6, 2008

DOI: 10.1214/EJP.v13-572

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