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H 1 Frozen and near-critical percolation

Auteurs : van den Berg, Jacob (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Motivated by solgel transitions, David Aldous (2000) introduced and analysed a fascinating dynamic percolation model on a tree where clusters stop growing ('freeze') as soon as they become infinite.
    In this talk I will discuss recent (and ongoing) work, with Demeter Kiss and Pierre Nolin, on processes of similar flavour on planar lattices. We focus on the problem whether or not the giant (i.e. 'frozen') clusters occupy a negligible fraction of space. Accurate results for near-critical percolation play an important role in the solution of this problem.
    I will also present a version of the model which can be interpreted as a sensor/communication network.

    Codes MSC :
    60K35 - Interacting random processes; statistical mechanics type models; percolation theory
    82B43 - Percolation (equilibrium statistical mechanics)

    Informations sur la rencontre

    Nom du congrès : Dynamics on random graphs and random maps / Dynamiques sur graphes et cartes aléatoires
    Organisteurs Congrès : Ménard, Laurent ; Nolin, Pierre ; Schapira, Bruno ; Singh, Arvind
    Dates : 23/10/2017 - 27/10/2017
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1672.html

    Citation Data

    DOI : 10.24350/CIRM.V.19230203
    Cite this video as: van den Berg, Jacob (2017). Frozen and near-critical percolation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19230203
    URI : http://dx.doi.org/10.24350/CIRM.V.19230203

    Voir aussi


    1. van den Berg, J., & Nolin, P. (2017). Two-dimensional volume-frozen percolation: exceptional scales. The Annals of Applied Probability, 27(1), 91-108 - http://dx.doi.org/10.1214/16-AAP1198