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Unicellular maps vs hyperbolic surfaces in high genus
Multi angle
Authors : Louf, Baptiste (Author of the conference)
CIRM (Publisher )
05C10 - Planar graphs; geometric and topological aspects of graph theory
05C80 - Random graphs
60C05 - Combinatorial probability
60D05 - Geometric probability and stochastic geometry
Additional resources :
https://www.cirm-math.fr/RepOrga/2528/Slides/Pres.pdf
CIRM (Publisher )
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Abstract :
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.
Keywords : large genus; random maps; hyperbolic surfaces
MSC Codes : 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.
Keywords : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/2528/Slides/Pres.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/02/2022 Conference Date : 17/01/2022 Subseries : Research talks arXiv category : Probability ; Combinatorics ; Geometric Topology Mathematical Area(s) : Combinatorics ; Probability & Statistics ; Topology Format : MP4 (.mp4) - HD Video Time : 00:49:19 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-17_Louf.mp4 
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Information on the Event
Event Title : Random Geometry / Géométrie aléatoireEvent Organizers : Curien, Nicolas ; Goldschmidt, Christina ; Le Gall, Jean-François ; Miermont, Grégory ; Rhodes, Rémi Dates : 17/01/2022 - 21/01/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2528.html
Citation Data
DOI : 10.24350/CIRM.V.19876203Cite this video as: 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 |
See Also
- [Multi angle] Some questions on the Brownian Map motivated by its higher-genus analogues / Author of the conference Chapuy, Guillaume.
- [Multi angle] Height coupled trees / Author of the conference Ünel, Meltem.
- [Multi angle] Growing maps face by face / Author of the conference Caraceni, Alessandra.
- [Multi angle] Resolution of Liouville CFT : Segal axioms and bootstrap / Author of the conference Guillarmou, Colin.
- [Multi angle] Conformal bootstrap in Liouville theory / Author of the conference Vargas, Vincent.
- [Multi angle] Maps, Hurwitz numbers and formulas for free probability at all genera / Author of the conference Borot, Gaëtan.
- [Multi angle] Generalised Kontsevich graphs, topological recursion and r-spin intersection numbers / Author of the conference Garcia-Failde, Elba.
- [Multi angle] Multicritical Schur measures / Author of the conference Bouttier, Jérémie.
- [Multi angle] The scaling limit of random planar maps with large faces / Author of the conference Riera, Armand.
- [Multi angle] Random hyperbolic surfaces / Author of the conference Budd, Timothy.
- [Multi angle] Bijections for maps on non-oriented surfaces / Author of the conference Dołęga, Maciej.
- [Multi angle] Nonbijective scaling limit of maps via restriction / Author of the conference Bettinelli, Jérémie.
- [Multi angle] The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity / Author of the conference Borga, Jacopo.
- [Multi angle] Geometry of the sign clusters in the Infinite Ising-weighted triangulation / Author of the conference Albenque, Marie.
Bibliography
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