English
Unicellular maps vs hyperbolic surfaces in high genus
Multi angle
Auteurs : Louf, Baptiste (Auteur de la conférence)
CIRM (Editeur )
05C10 - Planar graphs; geometric and topological aspects of graph theory
05C80 - Random graphs
60C05 - Combinatorial probability
60D05 - Geometric probability and stochastic geometry
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2528/Slides/Pres.pdf
CIRM (Editeur )
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Résumé :
In the past few years, the study of the geometric properties of random maps has been extended to a new regime, the 'high genus regime', where we are interested in maps whose size and genus tend to infinity at the same time, at the same rate.
We consider here a slightly different case, where the genus also tends to infinity, but less rapidly than the size, and we study the law of simple cycles (with a well-chosen rescaling of the graph distance) in unicellular maps (maps with one face), thanks to a powerful bijection of Chapuy, Féray and Fusy.
The interest of this work is that we obtain exactly the same law as Mirzakhani and Petri who counted closed geodesics on a model of random hyperbolic surfaces in large genus (the Weil- Petersson measure). This leads us to conjecture that these two models are somehow 'the same' in the limit.
Mots-Clés : large genus; random maps; hyperbolic surfaces
Codes MSC : We consider here a slightly different case, where the genus also tends to infinity, but less rapidly than the size, and we study the law of simple cycles (with a well-chosen rescaling of the graph distance) in unicellular maps (maps with one face), thanks to a powerful bijection of Chapuy, Féray and Fusy.
The interest of this work is that we obtain exactly the same law as Mirzakhani and Petri who counted closed geodesics on a model of random hyperbolic surfaces in large genus (the Weil- Petersson measure). This leads us to conjecture that these two models are somehow 'the same' in the limit.
Mots-Clés : large genus; random maps; hyperbolic surfaces
05C10 - Planar graphs; geometric and topological aspects of graph theory
05C80 - Random graphs
60C05 - Combinatorial probability
60D05 - Geometric probability and stochastic geometry
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2528/Slides/Pres.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 04/02/2022 Date de Captation : 17/01/2022 Sous Collection : Research talks Catégorie arXiv : Probability ; Combinatorics ; Geometric Topology Domaine(s) : Combinatoires ; Probabilités & Statistiques ; Topologie Format : MP4 (.mp4) - HD Durée : 00:49:19 Audience : Chercheurs Download : https://videos.cirm-math.fr/2022-01-17_Louf.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Random Geometry / Géométrie aléatoireOrganisateurs de la Rencontre : Curien, Nicolas ; Goldschmidt, Christina ; Le Gall, Jean-François ; Miermont, Grégory ; Rhodes, Rémi Dates : 17/01/2022 - 21/01/2022 Année de la rencontre : 2022 URL de la Rencontre : https://conferences.cirm-math.fr/2528.html
Données de citation
DOI : 10.24350/CIRM.V.19876203Citer cette vidéo: Louf, Baptiste (2022). Unicellular maps vs hyperbolic surfaces in high genus. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19876203 URI : http://dx.doi.org/10.24350/CIRM.V.19876203 |
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