  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.
