Displaying similar documents to “Shape transition under excess self-intersections for transient random walk”

Limit laws for the energy of a charged polymer

Xia Chen (2008)

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

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In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy =∑ 1 of the polymer { , …, } equipped with random electrical charges { , …, }. Our approach is based on comparison of the moments between and the self-intersection local time =∑1 run by the...

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

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...

Local limit theorems on some non unimodular groups.

Emile Le Page, Marc Peigné (1999)

Revista Matemática Iberoamericana

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Let Gd be the semi-direct product of R*+ and Rd, d ≥ 1 and let us consider the product group Gd,N = Gd x RN, N ≥ 1. For a large class of probability measures μ on Gd,N, one prove that there exists ρ(μ) ∈ ]0,1] such that the sequence of finite measures {(n(N+3)/2 / ρ(μ)n) μ*n...

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...

Disorder relevance for the random walk pinning model in dimension 3

Matthias Birkner, Rongfeng Sun (2011)

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

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We study the continuous time version of the , where conditioned on a continuous time random walk ( )≥0 on ℤ with jump rate > 0, which plays the role of disorder, the law up to time of a second independent random walk ( )0≤≤ with jump rate 1 is Gibbs transformed with weight e (,), where (, ) is the collision local time between and up to time . As the inverse temperature varies, the model undergoes a localization–delocalization...