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
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.
@article{AIHPB_2010__46_1_250_0,
     author = {Asselah, Amine},
     title = {Shape transition under excess self-intersections for transient random walk},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {1},
     year = {2010},
     pages = {250-278},
     doi = {10.1214/09-AIHP318},
     zbl = {1202.60151},
     mrnumber = {2641778},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2010__46_1_250_0}
}
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. https://www.numdam.org/item/AIHPB_2010__46_1_250_0/

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