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

2008/01/12 by Elena Kosygina, Kosygina, Elena, Martin Zerner +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #60J80 #60K35 #60K37 #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0801.1924

openalex publication_date 2008/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Excited random walk in three dimensions has positive speed

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