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Hyperbolic Voronoi percolation

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Auteurs : Müller, Tobias (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : I will discuss percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. That is, to each point $z$ of a constant intensity Poisson point process Z on the hyperbolic plane we assign its Voronoi cell – the region consisting of all points that are closer to z than to any other $z'$ in $Z$ –and we colour each cell black with probability p and white with probability 1 - p, independently of the colours of all other cells. We say that percolation occurs if there is an infinite connected cluster of black cells.Hyperbolic Poisson-Voronoi percolation was first studied by Benjamini and Schramm about twenty years ago. Their results show that there are spectacular differences with the corresponding model in the Euclidean plane.I will sketch joint work with my recently graduated doctoral student Ben Hansen that resolves a conjecture and an open question, posed by Benjamini and Schramm, on the behaviour of the “critical probability for percolation” as a function of the intensity parameter of the underlying Poisson process. (Unlike in Euclidean Poisson-Voronoi percolation, this critical value depends on the intensity of the underlying Poisson process.) Based on joint work with Benjamin Hansen.

Codes MSC :
60K35 - Interacting random processes; statistical mechanics type models; percolation theory

    Informations sur la Vidéo

    Réalisateur : Recanzone, Luca
    Langue : Anglais
    Date de publication : 23/10/2023
    Date de captation : 05/10/2023
    Sous collection : Research talks
    arXiv category : Probability ; Combinatorics
    Domaine : Combinatorics ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:49:53
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2023-10-05_Muller.mp4

Informations sur la Rencontre

Nom de la rencontre : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens
Organisateurs de la rencontre : Curien, Nicolas ; Garcia-Failde, Elba ; Petri, Bram ; Singh, Arvind
Dates : 02/10/2023 - 06/10/2023
Année de la rencontre : 2023
URL Congrès : https://conferences.cirm-math.fr/2897.html

Données de citation

DOI : 10.24350/CIRM.V.20099703
Citer cette vidéo: Müller, Tobias (2023). Hyperbolic Voronoi percolation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20099703
URI : http://dx.doi.org/10.24350/CIRM.V.20099703

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