English
Some questions on the Brownian Map motivated by its higher-genus analogues
Multi angle
Auteurs : Chapuy, Guillaume (Auteur de la Conférence)
CIRM (Editeur )
05A15 - Exact enumeration problems, generating functions
05A16 - Asymptotic enumeration
05C80 - Random graphs
60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
60J85 - Applications of branching processes
CIRM (Editeur )
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Résumé :
Several operations of combinatorial surgery can be used to relate maps of a given genus g to maps of genus g' is smaller than g. One of them is the Tutte/Lehman-Walsh decomposition, but more advanced constructions exist in the combinatorial toolbox, based on the Marcus-Schaeffer/ Miermont or the trisection bijections.
At the asymptotic level, these constructions lead to surprising relations between the enumeration of maps of genus g, and the genus 0 Brownian map. I will talk about some fascinating identities and (open) problems resulting from these connections, related to Voronoi diagrams, 'W-functionals', and properties of the ISE measure. Although the motivation comes from 'higher genus', these questions deal with the usual Brownian map as everyone likes it.
This is not very new material, and a (mostly French) part of the audience may have heard these stories one million times. But still I hope it will be interesting to advertise them here. In particular, I do not know if recent 'Liouville-based' approaches have anything to say about all this.
Keywords : random maps; high-genus maps; Brownian maps; Voronoï diagrams; bijections; trisections
Codes MSC : At the asymptotic level, these constructions lead to surprising relations between the enumeration of maps of genus g, and the genus 0 Brownian map. I will talk about some fascinating identities and (open) problems resulting from these connections, related to Voronoi diagrams, 'W-functionals', and properties of the ISE measure. Although the motivation comes from 'higher genus', these questions deal with the usual Brownian map as everyone likes it.
This is not very new material, and a (mostly French) part of the audience may have heard these stories one million times. But still I hope it will be interesting to advertise them here. In particular, I do not know if recent 'Liouville-based' approaches have anything to say about all this.
Keywords : random maps; high-genus maps; Brownian maps; Voronoï diagrams; bijections; trisections
05A15 - Exact enumeration problems, generating functions
05A16 - Asymptotic enumeration
05C80 - Random graphs
60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
60J85 - Applications of branching processes
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 04/02/2022 Date de captation : 20/01/2022 Sous collection : Research talks arXiv category : Probability ; Combinatorics Domaine : Combinatorics ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:52:16 Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2022-01-20_Chapuis.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 Congrès : https://conferences.cirm-math.fr/2528.html
Données de citation
DOI : 10.24350/CIRM.V.19884603Citer cette vidéo: Chapuy, Guillaume (2022). Some questions on the Brownian Map motivated by its higher-genus analogues. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19884603 URI : http://dx.doi.org/10.24350/CIRM.V.19884603 |
Voir aussi
- [Multi angle] Height coupled trees / Auteur de la Conférence Ünel, Meltem.
- [Multi angle] Growing maps face by face / Auteur de la Conférence Caraceni, Alessandra.
- [Multi angle] Resolution of Liouville CFT : Segal axioms and bootstrap / Auteur de la Conférence Guillarmou, Colin.
- [Multi angle] Conformal bootstrap in Liouville theory / Auteur de la Conférence Vargas, Vincent.
- [Multi angle] Maps, Hurwitz numbers and formulas for free probability at all genera / Auteur de la Conférence Borot, Gaëtan.
- [Multi angle] Generalised Kontsevich graphs, topological recursion and r-spin intersection numbers / Auteur de la Conférence Garcia-Failde, Elba.
- [Multi angle] Multicritical Schur measures / Auteur de la Conférence Bouttier, Jérémie.
- [Multi angle] The scaling limit of random planar maps with large faces / Auteur de la Conférence Riera, Armand.
- [Multi angle] Random hyperbolic surfaces / Auteur de la Conférence Budd, Timothy.
- [Multi angle] Unicellular maps vs hyperbolic surfaces in high genus / Auteur de la Conférence Louf, Baptiste.
- [Multi angle] Bijections for maps on non-oriented surfaces / Auteur de la Conférence Dołęga, Maciej.
- [Multi angle] Nonbijective scaling limit of maps via restriction / Auteur de la Conférence Bettinelli, Jérémie.
- [Multi angle] The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity / Auteur de la Conférence Borga, Jacopo.
- [Multi angle] Geometry of the sign clusters in the Infinite Ising-weighted triangulation / Auteur de la Conférence Albenque, Marie.
Bibliographie
- CHAPUY, Guillaume. The structure of unicellular maps, and a connection between maps of positive genus and planar labelled trees. Probability Theory and Related Fields, 2010, vol. 147, no 3, p. 415-447. - http://dx.doi.org/10.1007/s00440-009-0211-0
- CHAPUY, Guillaume. On tessellations of random maps and the $$ t_g $$ tg-recurrence. Probability Theory and Related Fields, 2019, vol. 174, no 1, p. 477-500. - http://dx.doi.org/10.1007/s00440-018-0865-6
- ADDARIO-BERRY, Louigi, ANGEL, Omer, CHAPUY, Guillaume, et al. Voronoi tessellations in the CRT and continuum random maps of finite excess. In : Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2018. p. 933-946. - https://doi.org/10.1137/1.9781611975031.60
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