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.
Publié le : 2010-02-15
Classification:
Self-intersection local times,
Large deviations,
Random walk,
60K35,
82C22,
60J25
@article{1267454116,
author = {Asselah, Amine},
title = {Shape transition under excess self-intersections for transient random walk},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 250-278},
language = {en},
url = {http://dml.mathdoc.fr/item/1267454116}
}
Asselah, Amine. Shape transition under excess self-intersections for transient random walk. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 250-278. http://gdmltest.u-ga.fr/item/1267454116/