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Frozen and near-critical percolation
Multi angle
Authors : van den Berg, Jacob (Author of the conference)
CIRM (Publisher )
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
82B43 - Percolation (equilibrium statistical mechanics)
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 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.
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 : 26/10/2017 Conference Date : 25/10/2017 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:58:16 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-10-25_Van_Den_Berg.mp4 
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Information on the Event
Event Title : Dynamics on random graphs and random maps / Dynamiques sur graphes et cartes aléatoiresEvent Organizers : Ménard, Laurent ; Nolin, Pierre ; Schapira, Bruno ; Singh, Arvind Dates : 23/10/2017 - 27/10/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1672.html
Citation Data
DOI : 10.24350/CIRM.V.19230203Cite 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 |
See Also
- [Post-edited] Bootstrap percolation on Erdos-Renyi graphs / Author of the conference Angel, Omer.
- [Multi angle] Extinction time for the weaker of two competing stochastic SIS logistic epidemics / Author of the conference Luczak, Malwina.
- [Multi angle] Interlacements and the uniform spanning forest / Author of the conference Hutchcroft, Tom.
- [Multi angle] Weighted distances in scale free random graphs / Author of the conference Komjathy, Julia.
Bibliography
- 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
