Nous considérons un modèle de marches aléatoires en milieu aléatoire ayant pour sommets un sous-ensemble aléatoire de et une probabilité de transition uniforme sur points (les plus proches voisins dans chacune des directions des coordonnées). Nous prouvons que la vitesse de ce type de marches est presque sûrement zéro, donnons une caractérisation partielle de transience et récurrence dans les différentes dimensions et prouvons un théorème central limite (CLT) pour de telles marches sous une condition concernant la distance entre plus proches voisins.
We consider a model for random walks on random environments (RWRE) with a random subset of as the vertices, and uniform transition probabilities on points (the closest in each of the coordinate directions). We prove that the velocity of such random walks is almost surely zero, give partial characterization of transience and recurrence in the different dimensions and prove a Central Limit Theorem (CLT) for such random walks, under a condition on the distance between coordinate nearest neighbors.
Mots clés : discrete point processes, random walk in random environment
@article{AIHPB_2015__51_2_727_0, author = {Berger, Noam and Rosenthal, Ron}, title = {Random walks on discrete point processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {727--755}, publisher = {Gauthier-Villars}, volume = {51}, number = {2}, year = {2015}, doi = {10.1214/13-AIHP593}, mrnumber = {3335023}, zbl = {1315.60115}, language = {en}, url = {http://www.numdam.org/articles/10.1214/13-AIHP593/} }
TY - JOUR AU - Berger, Noam AU - Rosenthal, Ron TI - Random walks on discrete point processes JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2015 SP - 727 EP - 755 VL - 51 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/13-AIHP593/ DO - 10.1214/13-AIHP593 LA - en ID - AIHPB_2015__51_2_727_0 ER -
%0 Journal Article %A Berger, Noam %A Rosenthal, Ron %T Random walks on discrete point processes %J Annales de l'I.H.P. Probabilités et statistiques %D 2015 %P 727-755 %V 51 %N 2 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/13-AIHP593/ %R 10.1214/13-AIHP593 %G en %F AIHPB_2015__51_2_727_0
Berger, Noam; Rosenthal, Ron. Random walks on discrete point processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 2, pp. 727-755. doi : 10.1214/13-AIHP593. http://www.numdam.org/articles/10.1214/13-AIHP593/
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