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Self-interacting walks and uniform spanning forests
Post-edited
Authors : Peres, Yuval (Author of the conference)
CIRM (Publisher )
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 (Publisher )
Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 08/06/17 Conference Date : 31/05/2017 Subseries : Research talks arXiv category : Probability ; Mathematical Physics ; Combinatorics Mathematical Area(s) : Combinatorics ; Probability & Statistics ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:58:59 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-05-31_Peres.mp4 
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Information on the Event
Event Title : Random walks with memory / Marches aléatoires à mémoireEvent Organizers : Gantert, Nina ; Ramirez, Alejandro ; Sabot, Christophe ; Tarres, Pierre ; Toth, Balint Dates : 29/05/17 - 02/06/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1566.html
Citation Data
DOI : 10.24350/CIRM.V.19179503Cite 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 |
See Also
- [Multi angle] Internal diffusion-limited aggregation with random starting points / Author of the conference Kozma, Gady.
- [Multi angle] Introduction to hyperbolic sigma models and Edge Reinforced Random Walk / Author of the conference Spencer, Tom.
- [Multi angle] Time changes of stochastic processes: convergence and heat kernel estimates / Author of the conference Kumagai, Takashi.
Bibliography
- Komjathy, J., & Peres, Y. (2015). Topics in Markov chains: mixing and escape rate.
