[Temps passé dans une boule pour une marche aléatoire branchante critique]
Nous étudions la queue de distribution du temps passé dans une boule par une marche aléatoire branchante critique. Notre étude apporte un éclairage nouveau aux résultats récents de Angel, Hutcroft et Jarai, en particulier sur le cas de la dimension 4. Enfin nous étudions également le nombre de particules déposées sur la frontière d’une boule.
We study a critical branching random walk on . We focus on the tail of the time spent in a ball, and our study, in dimension four and higher, sheds new light on the recent result of Angel, Hutchcroft and Jarai [AHJ21], in particular on the special features of the critical dimension four. Finally, we analyze the number of walks transported by the branching random walk on the boundary of a distant ball.
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Keywords: Branching random walk, local times, range
Mot clés : Marches aléatoires branchantes, temps local, amplitude
Amine Asselah 1 ; Bruno Schapira 2
CC-BY 4.0
@article{JEP_2024__11__1441_0,
author = {Amine Asselah and Bruno Schapira},
title = {Time spent in a ball by a~critical~branching~random walk},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1441--1481},
publisher = {\'Ecole polytechnique},
volume = {11},
year = {2024},
doi = {10.5802/jep.281},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.281/}
}
TY - JOUR AU - Amine Asselah AU - Bruno Schapira TI - Time spent in a ball by a critical branching random walk JO - Journal de l’École polytechnique — Mathématiques PY - 2024 SP - 1441 EP - 1481 VL - 11 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.281/ DO - 10.5802/jep.281 LA - en ID - JEP_2024__11__1441_0 ER -
%0 Journal Article %A Amine Asselah %A Bruno Schapira %T Time spent in a ball by a critical branching random walk %J Journal de l’École polytechnique — Mathématiques %D 2024 %P 1441-1481 %V 11 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.281/ %R 10.5802/jep.281 %G en %F JEP_2024__11__1441_0
Amine Asselah; Bruno Schapira. Time spent in a ball by a critical branching random walk. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1441-1481. doi : 10.5802/jep.281. https://jep.centre-mersenne.org/articles/10.5802/jep.281/
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