Displaying similar documents to “Asymptotics of a dynamic random walk in a random scenery : I. Law of large numbers”

Shape transition under excess self-intersections for transient random walk

Amine Asselah (2010)

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

Similarity:

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.

Normalizing constants for a statistic based on logarithms of disjoint m-spacings

Franciszek Czekała (1996)

Applicationes Mathematicae

Similarity:

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].

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

Similarity:

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...