A limit law for random walk in a random environment
H. Kesten, M. V. Kozlov, F. Spitzer (1975)
Compositio Mathematica
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H. Kesten, M. V. Kozlov, F. Spitzer (1975)
Compositio Mathematica
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Alexander R. Pruss (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Rastislav Potocký, Marta Urbaníková (1999)
Mathematica Slovaca
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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...
A. J. Stam (1971)
Compositio Mathematica
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Ross G. Pinsky (2010)
Annales de l'I.H.P. Probabilités et statistiques
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Consider a variant of the simple random walk on the integers, with the following transition mechanism. At each site , the probability of jumping to the right is ()∈[½, 1), until the first time the process jumps to the left from site , from which time onward the probability of jumping to the right is ½. We investigate the transience/recurrence properties of this process in both deterministic and stationary, ergodic environments {()}∈. In deterministic environments, we also study the speed...