English
Self-interacting walks and uniform spanning forests
Post-edited
Auteurs : Peres, Yuval (Auteur de la Conférence)
CIRM (Editeur )
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)
CIRM (Editeur )
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)
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 08/06/17 Date de captation : 31/05/2017 Sous collection : Research talks arXiv category : Probability ; Mathematical Physics ; Combinatorics Domaine : Combinatorics ; Probability & Statistics ; Mathematical Physics Format : MP4 (.mp4) - HD Durée : 00:58:59 Audience : Researchers Download : https://videos.cirm-math.fr/2017-05-31_Peres.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Random walks with memory / Marches aléatoires à mémoireOrganisateurs de la rencontre : 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
Données de citation
DOI : 10.24350/CIRM.V.19179503Citer cette vidéo: 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
- [Multi angle] Internal diffusion-limited aggregation with random starting points / Auteur de la Conférence Kozma, Gady.
- [Multi angle] Introduction to hyperbolic sigma models and Edge Reinforced Random Walk / Auteur de la Conférence Spencer, Tom.
- [Multi angle] Time changes of stochastic processes: convergence and heat kernel estimates / Auteur de la Conférence Kumagai, Takashi.
Bibliographie
- Komjathy, J., & Peres, Y. (2015). Topics in Markov chains: mixing and escape rate.
