We consider excited random walks (ERWs) on ℤ 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 [15] have shown that when the total expected drift per site, δ, is larger than 1 then ERW is transient to the right and, moreover, for δ>4 under the averaged measure it obeys the Central Limit Theorem. We show that when δ∈(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 δ/2. Our method also extends the results obtained by Basdevant and Singh [2] for δ∈(1, 2] under the non-negativity assumption to the setting which allows both positive and negative cookies.
Publié le : 2011-05-15
Classification:
Excited random walk,
Limit theorem,
Stable law,
Branching process,
Diffusion approximation,
60K37,
60F05,
60J80,
60J60
@article{1300887283,
author = {Kosygina, Elena and Mountford, Thomas},
title = {Limit laws of transient excited random walks on integers},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {47},
number = {1},
year = {2011},
pages = { 575-600},
language = {en},
url = {http://dml.mathdoc.fr/item/1300887283}
}
Kosygina, Elena; Mountford, Thomas. Limit laws of transient excited random walks on integers. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp. 575-600. http://gdmltest.u-ga.fr/item/1300887283/