Kosygina, Elena; Mountford, Thomas Limit laws of transient excited random walks on integers. (English. French summary) Zbl 1215.60057 Ann. Inst. Henri Poincaré, Probab. Stat. 47, No. 2, 575-600 (2011). Summary: We consider excited random walks (ERWs) on \(\mathbb Z\) with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. E. Kosygina and M. P. W. Zerner [Electron. J. Probab. 13, 1952–1979 (2008; Zbl 1191.60113)] 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 A.-L. Basdevant and A. 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