no. 5
Non-noise sensitivity for word hyperbolic groups
Tanaka, Ryokichi1
1Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 5, pp. 1487-1510

We show that non-elementary random walks on word hyperbolic groups with finite first moment are not noise sensitive in a strong sense for small noise parameters.

Nous montrons que les marches aléatoires non élémentaires sur des groupes hyperboliques au sens de Gromov ayant un premier moment fini ne sont pas sensibles au bruit au sens fort pour de petits paramètres de bruit.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1803

Tanaka, Ryokichi  1

1 Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Tanaka, Ryokichi. Non-noise sensitivity for word hyperbolic groups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 5, pp. 1487-1510. doi: 10.5802/afst.1803

[1] Benjamini, Itai; Brieussel, Jérémie Noise sensitivity of random walks on groups, ALEA Lat. Am. J. Probab. Math. Stat., Volume 20 (2023) no. 2, pp. 1139-1164 | DOI | MR

[2] Bonk, Mario; Schramm, Oded Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal., Volume 10 (2000) no. 2, pp. 266-306 | DOI | MR | Zbl

[3] Derriennic, Yves Quelques applications du théorème ergodique sous-additif, Conference on Random Walks (Kleebach, 1979) (Astérisque), Volume 74, Société Mathématique de France, 1980, pp. 183-201 | Zbl | MR | Numdam

[4] Derriennic, Yves Entropie, théorèmes limite et marches aléatoires, Probability measures on groups, VIII (Oberwolfach, 1985) (Lecture Notes in Mathematics), Volume 1210, Springer, 1986, pp. 241-284 | DOI | MR | Zbl

[5] Erschler, Anna; Kaimanovich, Vadim A. Continuity of asymptotic characteristics for random walks on hyperbolic groups, Funkts. Anal. Prilozh., Volume 47 (2013) no. 2, pp. 84-89 | DOI | MR | Zbl

[6] Sur les groupes hyperboliques d’après Mikhael Gromov (Ghys, Étienne; de la Harpe, Pierre, eds.), Progress in Mathematics, 83, Birkhäuser, 1990 (papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988) | DOI | MR | Zbl

[7] Gromov, Mikhael L. Hyperbolic groups, Essays in group theory (Gersten, Stephen M., ed.) (Mathematical Sciences Research Institute Publications), Volume 8, Springer, 1987, pp. 75-263 | Zbl | DOI

[8] Kaimanovich, Vadim A. The Poisson formula for groups with hyperbolic properties, Ann. Math. (2), Volume 152 (2000) no. 3, pp. 659-692 | DOI | MR | Zbl

[9] Kaimanovich, Vadim A.; Vershik, Anatoliĭ M. Random walks on discrete groups: boundary and entropy, Ann. Probab., Volume 11 (1983) no. 3, pp. 457-490 | DOI | MR | Zbl

[10] Kalai, Gil Three puzzles on mathematics, computation, and games, Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. I. Plenary lectures, World Scientific; Sociedade Brasileira de Matemática, 2018, pp. 551-606 | DOI | MR | Zbl

[11] Tanaka, Ryokichi Dimension of harmonic measures in hyperbolic spaces, Ergodic Theory Dyn. Syst., Volume 39 (2019) no. 2, pp. 474-499 | DOI | MR | Zbl

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