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Post-edited Self-interacting walks and uniform spanning forests

Auteurs : Peres, Yuval (Auteur de la Conférence)
CIRM (Editeur )

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Eulerian Walkers / rotor walks range size comb lattice mirror model critical percolation balanced exited walks Lyapunov function uniform spanning trees uniform spanning forests Wilson's agorithm / loop-erased random walks phase transition hypergraphs question of the audience

Résumé : In the first half of the talk, I will survey results and open problems on transience of self-interacting martingales. In particular, I will describe joint works with S. Popov, P. Sousi, R. Eldan and F. Nazarov on the tradeoff between the ambient dimension and the number of different step distributions needed to obtain a recurrent process. In the second, unrelated, half of the talk, I will present joint work with Tom Hutchcroft, showing that the component structure of the uniform spanning forest in $\mathbb{Z}^d$ changes every dimension for $d > 8$. This sharpens an earlier result of Benjamini, Kesten, Schramm and the speaker (Annals Math 2004), where we established a phase transition every four dimensions. The proofs are based on a the connection to loop-erased random walks.

Codes MSC :
05C05 - Trees
05C80 - Random graphs
60G50 - Sums of independent random variables; random walks
60J10 - Markov chains (discrete-time Markov processes on discrete state spaces)
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
82B43 - Percolation (equilibrium statistical mechanics)

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 08/06/17
    Date de captation : 31/05/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:58:59
    Domaine : Combinatorics ; Probability & Statistics ; Mathematical Physics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-05-31_Peres.mp4

Informations sur la rencontre

Nom du congrès : Random walks with memory / Marches aléatoires à mémoire
Organisteurs Congrès : Gantert, Nina ; Ramirez, Alejandro ; Sabot, Christophe ; Tarres, Pierre ; Toth, Balint
Dates : 29/05/17 - 02/06/2017
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1566.html

Citation Data

DOI : 10.24350/CIRM.V.19179503
Cite this video as: Peres, Yuval (2017). Self-interacting walks and uniform spanning forests. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19179503
URI : http://dx.doi.org/10.24350/CIRM.V.19179503

Voir aussi

Bibliographie

  1. Komjathy, J., & Peres, Y. (2015). Topics in Markov chains: mixing and escape rate. <arXiv:1506.04850> - https://arxiv.org/abs/1506.04850



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