A local limit theorem on the semi-direct product of and
Émile Le Page, Marc Peigné (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Émile Le Page, Marc Peigné (1997)
Annales de l'I.H.P. Probabilités et statistiques
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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.
Rafał Latała, Krzysztof Oleszkiewicz (1995)
Colloquium Mathematicae
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Franciszek Czekała (1996)
Applicationes Mathematicae
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The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].
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...
Olivier Catoni (2003)
Annales de l'I.H.P. Probabilités et statistiques
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