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Maps, Hurwitz numbers and formulas for free probability at all genera
Multi angle
Authors : Borot, Gaëtan (Author of the conference)
CIRM (Publisher )
05A18 - Partitions of sets
06A07 - Combinatorics of partially ordered sets
46L54 - Free probability and free operator algebras
15B52 - Random matrices
16R60 - Functional identities (associative rings and algebras)
CIRM (Publisher )
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Abstract :
I will talk about a transformation involving double monotone Hurwitz numbers, which has several interpretations: transformation from maps to fully simple maps, passing from cumulants to free cumulants in free probability, action of an operator in the Fock space, symplectic exchange in topological recursion. In combination with recent work of Bychkov, Dunin-Barkowski, Kazarian and Shadrin, we deduce functional relations relating the generating series of higher order cumulants and free cumulants. This solves a 15-year old problem posed by Collins, Mingo, Sniady and Speicher (the first order is Voiculescu R-transform). This leads us to a general theory of 'surfaced' freeness, which captures the all order asymptotic expansions in unitary invariant random matrix models, which can be described both from the combinatorial and the analytic perspective.
Based on https://arxiv.org/abs/2112.12184 with Séverin Charbonnier, Elba Garcia-Failde, Felix Leid and Sergey Shadrin.
Keywords : free cumulants; combinatorics; Hurwitz numbers; asymptotic expansion; random matrices
MSC Codes : Based on https://arxiv.org/abs/2112.12184 with Séverin Charbonnier, Elba Garcia-Failde, Felix Leid and Sergey Shadrin.
Keywords : free cumulants; combinatorics; Hurwitz numbers; asymptotic expansion; random matrices
05A18 - Partitions of sets
06A07 - Combinatorics of partially ordered sets
46L54 - Free probability and free operator algebras
15B52 - Random matrices
16R60 - Functional identities (associative rings and algebras)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/02/2022 Conference Date : 18/01/2022 Subseries : Research talks arXiv category : Operator Algebras ; Cryptography and Security Mathematical Area(s) : Combinatorics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:57:25 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-18_Borot.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.19877703Cite this video as: Borot, Gaëtan (2022). Maps, Hurwitz numbers and formulas for free probability at all genera. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19877703 URI : http://dx.doi.org/10.24350/CIRM.V.19877703 |
See Also
- [Multi angle] Some questions on the Brownian Map motivated by its higher-genus analogues / Author of the conference Chapuy, Guillaume.
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- [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.
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- [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] Unicellular maps vs hyperbolic surfaces in high genus / Author of the conference Louf, Baptiste.
- [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.
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Bibliography
- BOROT, Gaëtan, CHARBONNIER, Séverin, GARCIA-FAILDE, Elba, et al. Analytic theory of higher order free cumulants. arXiv preprint arXiv:2112.12184, 2021. - https://arxiv.org/abs/2112.12184
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