Covering problems and exceptional points for random walk and brownian motion

Zhan Shi

Séminaire Bourbaki (2004-2005)

  • Volume: 47, page 469-480
  • ISSN: 0303-1179

Abstract

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Random walk is a fundamental object in probability theory. One of the most interesting problems for random walk (as well as for brownian motion, its continuous-time analogue) is to know how it covers various sets, where the frequently/rarely visited points lie, and whether there are many such points. Dembo, Peres, Rosen and Zeitouni solve several important open problems related to these questions.

How to cite

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Shi, Zhan. "Problèmes de recouvrement et points exceptionnels pour la marche aléatoire et le mouvement brownien." Séminaire Bourbaki 47 (2004-2005): 469-480. <http://eudml.org/doc/252175>.

@article{Shi2004-2005,
abstract = {La marche aléatoire (ou marche au hasard) est un objet fondamental de la théorie des probabilités. Un des problèmes les plus intéressants pour la marche aléatoire (ainsi que pour le mouvement brownien, son analogue dans un contexte continu) est de savoir comment elle recouvre des ensembles où se trouvent les points qui sont souvent (ou au contraire, rarement) visités, et combien il y a de tels points. Les travaux de Dembo, Peres, Rosen et Zeitouni permettent de résoudre plusieurs conjectures importantes liées à ces questions.},
author = {Shi, Zhan},
journal = {Séminaire Bourbaki},
keywords = {covering problem; favourite point; thick point; thin point; late point; multifractal analysis; occupation measure; tree; random walk; brownian motion},
language = {fre},
pages = {469-480},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Problèmes de recouvrement et points exceptionnels pour la marche aléatoire et le mouvement brownien},
url = {http://eudml.org/doc/252175},
volume = {47},
year = {2004-2005},
}

TY - JOUR
AU - Shi, Zhan
TI - Problèmes de recouvrement et points exceptionnels pour la marche aléatoire et le mouvement brownien
JO - Séminaire Bourbaki
PY - 2004-2005
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 47
SP - 469
EP - 480
AB - La marche aléatoire (ou marche au hasard) est un objet fondamental de la théorie des probabilités. Un des problèmes les plus intéressants pour la marche aléatoire (ainsi que pour le mouvement brownien, son analogue dans un contexte continu) est de savoir comment elle recouvre des ensembles où se trouvent les points qui sont souvent (ou au contraire, rarement) visités, et combien il y a de tels points. Les travaux de Dembo, Peres, Rosen et Zeitouni permettent de résoudre plusieurs conjectures importantes liées à ces questions.
LA - fre
KW - covering problem; favourite point; thick point; thin point; late point; multifractal analysis; occupation measure; tree; random walk; brownian motion
UR - http://eudml.org/doc/252175
ER -

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