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.
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...
Nicolas Petrelis (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a simple random walk of length , denoted by ( ), and we define ( ) a sequence of centered i.i.d. random variables. For ∈ℕ we define (( , …, )) an i.i.d sequence of random vectors. We set ∈ℝ, ≥0 and ≥0, and transform the measure on the set of random walk trajectories with the hamiltonian ∑ ( +)sign( )+∑ ∑ ...
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...
Richard Bass, Xia Chen, Jay Rosen (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We study functionals of the form = ⋯ | ( )+⋯+ ( )| d ⋯ d , where (), …, () are i.i.d. -dimensional symmetric stable processes of index 0<≤2. We obtain results about the large deviations and laws of the iterated logarithm for .