Positively and negatively excited random walks on integers, with branching processes. (English) Zbl 1191.60113

Kosygina, Elena; Zerner, Martin P. W.

Electron. J. Probab. 13, 1952-1979 (2008).

Summary: 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 [Probab. Theory Relat. Fields 133, No. 1, 98–122 (2005; Zbl 1076.60088)] and for positivity of speed by A.-L. Basdevant and A. Singh [Probab. Theory Relat. Fields 141, No. 3–4, 625–645 (2008; Zbl 1141.60383); Electron. J. Probab. 13, 811–851, electronic only (2008; Zbl 1191.60107)] 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.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60K37	Processes in random environments
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

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

Citations:

Zbl 1076.60088; Zbl 1141.60383; Zbl 1191.60107