[Déviations modérées pour le range d'une marche aléatoire transiente: concentration trajectorielle]
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.
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].
Keywords: Large deviations, capacity, range of a random walk, boundary of the range.
Mot 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},
publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
volume = {Ser. 4, 50},
number = {3},
year = {2017},
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. https://www.numdam.org/articles/10.24033/asens.2331/
A note on random walk in random scenery, Ann. Inst. H. Poincaré Probab. Statist., Volume 43 (2007), pp. 163-173 (ISSN: 0246-0203) | DOI | Numdam | MR | Zbl
Boundary of the range of transient random walk (preprint arXiv:1507.01031, to appear in Probab. Theory Related Fields ) | MR
On large intersection and self-intersection local times in dimension five or more (preprint arXiv:0801.3918 )
Capacity of the range of random walk on
Entropy of random walk range, Ann. Inst. Henri Poincaré Probab. Stat., Volume 46 (2010), pp. 1080-1092 (ISSN: 0246-0203) | DOI | Numdam | MR | Zbl
On the volume of the Wiener sausage, Ann. Probab., Volume 18 (1990), pp. 1576-1582 (ISSN: 0091-1798) | DOI | MR | Zbl
Localization of a two-dimensional random walk with an attractive path interaction, Ann. Probab., Volume 22 (1994), pp. 875-918 (ISSN: 0091-1798) | DOI | MR | Zbl
Condensation of random walks and the Wulff crystal (preprint arXiv:1305.0139 )
Asymptotics for the Wiener sausage, Comm. Pure Appl. Math., Volume 28 (1975), pp. 525-565 (ISSN: 0010-3640) | DOI | MR | Zbl
On the number of distinct sites visited by a random walk, Comm. Pure Appl. Math., Volume 32 (1979), pp. 721-747 (ISSN: 0010-3640) | DOI | MR | Zbl
Gaussian estimates for Markov chains and random walks on groups, Ann. Probab., Volume 21 (1993), pp. 673-709 (ISSN: 0091-1798) | DOI | MR | Zbl
On the range of random walk, Israel J. Math., Volume 6 (1968), pp. 373-380 (ISSN: 0021-2172) | DOI | MR | Zbl
, The Dynkin Festschrift (Progr. Probab.), Volume 34, Birkhäuser, 1994, pp. 167-184 | DOI | MR | Zbl
, Modern Birkhäuser Classics, Birkhäuser, 2013, 223 pages (reprint of the 1996 edition) (ISBN: 978-1-4614-5971-2; 978-1-4614-5972-9) | DOI | MR | Zbl
Propriétés d'intersection des marches aléatoires. I. Convergence vers le temps local d'intersection, Comm. Math. Phys., Volume 104 (1986), pp. 471-507 http://projecteuclid.org/euclid.cmp/1104115088 (ISSN: 0010-3616) | DOI | MR | Zbl
, Cambridge Studies in Advanced Math., 123, Cambridge Univ. Press, Cambridge, 2010, 364 pages (ISBN: 978-0-521-51918-2) | DOI | MR | Zbl
The inner boundary of random walk range, J. Math. Soc. Japan, Volume 68 (2016), pp. 939-959 (ISSN: 0025-5645) | DOI | MR | Zbl
Intersections of random walks (2012)
Confinement of Brownian motion among Poissonian obstacles in
Connectivity properties of random interlacement and intersection of random walks, ALEA Lat. Am. J. Probab. Math. Stat., Volume 9 (2012), pp. 67-83 (ISSN: 1980-0436) | MR | Zbl
Long time asymptotics for the shrinking Wiener sausage, Comm. Pure Appl. Math., Volume 43 (1990), pp. 809-820 (ISSN: 0010-3640) | DOI | MR | Zbl
On the confinement property of two-dimensional Brownian motion among Poissonian obstacles, Comm. Pure Appl. Math., Volume 44 (1991), pp. 1137-1170 (ISSN: 0010-3640) | DOI | MR | Zbl
Moderate deviations for the volume of the Wiener sausage, Ann. of Math., Volume 153 (2001), pp. 355-406 (ISSN: 0003-486X) | DOI | MR | Zbl
On the volume of the intersection of two Wiener sausages, Ann. of Math., Volume 159 (2004), pp. 741-782 (ISSN: 0003-486X) | DOI | MR | Zbl
Cité par Sources :
