[Déviations modérées pour le range d'une marche aléatoire transiente: concentration trajectorielle]
We study downward deviations of the boundary of the range of a transient walk on the Euclidean lattice. We describe the optimal strategy adopted by the walk in order to shrink the boundary of its range. The technics we develop apply equally well to the range, and provide pathwise statements for the Swiss cheese picture of Bolthausen, van den Berg and den Hollander [7].
Nous étudions les déviations qui réduisent la frontière du support d'une marche transiente sur le réseau euclidien. Nous décrivons en particulier une stratégie optimale pour réduire la frontière du support. Les techniques employées s'appliquent aussi bien au volume du support lui-même, et fournissent des énoncés mathématiques qui illustrent l'image du « fromage suisse » de Bolthausen, van den Berg et den Hollander.
Keywords: Large deviations, capacity, range of a random walk, boundary of the range.
Mots-clés : Grandes déviations, capacité, range d'une marche aléatoire, frontière du range.
@article{ASENS_2017__50_3_755_0,
author = {Asselah, Amine and Schapira, Bruno},
title = {Moderate deviations for the range of a transient random walk: path concentration},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {755--786},
year = {2017},
publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
volume = {Ser. 4, 50},
number = {3},
doi = {10.24033/asens.2331},
mrnumber = {3665554},
zbl = {1378.60055},
language = {en},
url = {https://www.numdam.org/articles/10.24033/asens.2331/}
}
TY - JOUR AU - Asselah, Amine AU - Schapira, Bruno TI - Moderate deviations for the range of a transient random walk: path concentration JO - Annales scientifiques de l'École Normale Supérieure PY - 2017 SP - 755 EP - 786 VL - 50 IS - 3 PB - Société Mathématique de France. Tous droits réservés UR - https://www.numdam.org/articles/10.24033/asens.2331/ DO - 10.24033/asens.2331 LA - en ID - ASENS_2017__50_3_755_0 ER -
%0 Journal Article %A Asselah, Amine %A Schapira, Bruno %T Moderate deviations for the range of a transient random walk: path concentration %J Annales scientifiques de l'École Normale Supérieure %D 2017 %P 755-786 %V 50 %N 3 %I Société Mathématique de France. Tous droits réservés %U https://www.numdam.org/articles/10.24033/asens.2331/ %R 10.24033/asens.2331 %G en %F ASENS_2017__50_3_755_0
Asselah, Amine; Schapira, Bruno. Moderate deviations for the range of a transient random walk: path concentration. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 3, pp. 755-786. doi: 10.24033/asens.2331
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