Maps, Hurwitz numbers and formulas for free probability at all genera | Vidéo | Carmin.tv

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Maps, Hurwitz numbers and formulas for free probability at all genera

De Gaëtan Borot

Apparaît dans la collection : Random Geometry / Géométrie aléatoire

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.

Informations sur la vidéo

Date de captation 18/01/2022
Date de publication 04/02/2022
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19877703
Citer cette vidéo Borot, Gaëtan (18/01/2022). Maps, Hurwitz numbers and formulas for free probability at all genera. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19877703
URL https://dx.doi.org/10.24350/CIRM.V.19877703

Domaine(s)

Bibliographie

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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