Limit laws of transient excited random walks on integers

Details Limit laws of transient excited random walks on integers Limit laws of transient excited random walks on integers

2009-08-30

arxiv.org/abs/0908.4356v3

Ann. Inst. H. Poincar\'e Probab. Stat., 47 (2011), no. 2, 575-600

Mathematics

Probability

27 pages

Scientific paper

10.1214/10-AIHP376

We consider excited random walks (ERWs) on integers with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [KZ08] have shown that when the total expected drift per site, delta, is larger than 1 then ERW is transient to the right and, moreover, for delta>4 under the averaged measure it obeys the Central Limit Theorem. We show that when delta in (2,4] the limiting behavior of an appropriately centered and scaled excited random walk under the averaged measure is described by a strictly stable law with parameter delta/2. Our method also extends the results obtained by Basdevant and Singh [BS08b] for delta in (1,2] under the non-negativity assumption to the setting which allows both positive and negative cookies.

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