Shape transition under excess self-intersections for transient random walk
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 1, pp. 250-278.

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.

DOI : 10.1214/09-AIHP318
Classification : 60K35, 82C22, 60J25
Mots-clés : self-intersection local times, large deviations, random walk 
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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, pp. 250-278. doi : 10.1214/09-AIHP318. http://www.numdam.org/articles/10.1214/09-AIHP318/

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