Displaying similar documents to “Transience/recurrence and the speed of a one-dimensional random walk in a “have your cookie and eat it” environment”

Limit laws of transient excited random walks on integers

Elena Kosygina, Thomas Mountford (2011)

Annales de l'I.H.P. Probabilités et statistiques

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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, , is larger than 1 then ERW is transient to the right and, moreover, for >4 under the averaged measure it obeys the Central Limit Theorem. We show that when ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited...

Shape transition under excess self-intersections for transient random walk

Amine Asselah (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We reveal a shape transition for a transient simple random walk forced to realize an excess -norm of the local times, as the parameter crosses the value ()=/(−2). Also, as an application of our approach, we establish a central limit theorem for the -norm of the local times in dimension 4 or more.

Moderate deviations for stationary sequences of bounded random variables

Jérôme Dedecker, Florence Merlevède, Magda Peligrad, Sergey Utev (2009)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of -mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.