Time spent in a ball by a critical branching random walk
[Temps passé dans une boule pour une marche aléatoire branchante critique]
Asselah, Amine1 ; Schapira, Bruno2
1LAMA, Univ Paris Est Créteil, Univ Gustave Eiffel, UPEM, CNRS, F-94010, Créteil, France & New York University at Shanghai
2Aix-Marseille Université, I2M, CNRS UMR 7373, 13453 Marseille, France & Université Lyon 1, Institut Camille Jordan, CNRS UMR 5208
Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1441-1481

We study a critical branching random walk on ℤ d . 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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.281
Classification : 60G50, 60J80
Keywords: Branching random walk, local times, range
Mots-clés : Marches aléatoires branchantes, temps local, amplitude

Asselah, Amine  1   ; Schapira, Bruno  2

1 LAMA, Univ Paris Est Créteil, Univ Gustave Eiffel, UPEM, CNRS, F-94010, Créteil, France & New York University at Shanghai
2 Aix-Marseille Université, I2M, CNRS UMR 7373, 13453 Marseille, France & Université Lyon 1, Institut Camille Jordan, CNRS UMR 5208
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Asselah, Amine; Schapira, Bruno. 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

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