Asselah, Amine
Shape transition under excess self-intersections for transient random walk
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 1 , p. 250-278
Zbl 1202.60151 | MR 2641778 | 1 citation dans Numdam
doi : 10.1214/09-AIHP318
URL stable : http://www.numdam.org/item?id=AIHPB_2010__46_1_250_0

Classification:  60K35,  82C22,  60J25
Nous décrivons un phénomène de transition de forme d'une marche aléatoire transiente forcée à réaliser une grande valeur de la norme-q du temps local, lorsque le paramètre q traverse la valeur critique qc(d)=d/(d-2). Comme application de notre approche, nous établissons un théorème de la limite centrale pour la norme-q du temps local en dimension 4 et plus.
We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d-2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.

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