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.
Mots clés : self-intersection local times, large deviations, random walk
@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}, pages = {250--278}, publisher = {Gauthier-Villars}, volume = {46}, number = {1}, year = {2010}, doi = {10.1214/09-AIHP318}, mrnumber = {2641778}, zbl = {1202.60151}, language = {en}, url = {http://www.numdam.org/articles/10.1214/09-AIHP318/} }
TY - JOUR AU - Asselah, Amine TI - Shape transition under excess self-intersections for transient random walk JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2010 SP - 250 EP - 278 VL - 46 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/09-AIHP318/ DO - 10.1214/09-AIHP318 LA - en ID - AIHPB_2010__46_1_250_0 ER -
%0 Journal Article %A Asselah, Amine %T Shape transition under excess self-intersections for transient random walk %J Annales de l'I.H.P. Probabilités et statistiques %D 2010 %P 250-278 %V 46 %N 1 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/09-AIHP318/ %R 10.1214/09-AIHP318 %G en %F 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. http://www.numdam.org/articles/10.1214/09-AIHP318/
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