English
The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity
Multi angle
Auteurs : Borga, Jacopo (Auteur de la Conférence)
CIRM (Editeur )
60D05 - Geometric probability and stochastic geometry
60G57 - Random measures
60H10 - Stochastic ordinary differential equations
CIRM (Editeur )
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Résumé :
Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permuton. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these results, mainly focusing on the case of pattern-avoiding permutations.
The main goal of the talk is to present a new family of universal limiting permutons, called skew Brownian permuton. This family includes (as particular cases) some already studied limiting permutons, such as the biased Brownian separable permuton and the Baxter permuton. We also show that some natural families of random constrained permutations converge to some new instances of the skew Brownian permuton.
The construction of these new limiting objects will lead us to investigate an intriguing connection with some perturbed versions of the Tanaka SDE and the SDEs encoding skew Brownian motions. We finally explain how it is possible to construct these new limiting permutons directly from a Liouville quantum gravity decorated with two SLE curves. Building on the latter connection, we compute the density of the intensity measure of the Baxter permuton.
Keywords : permutations; permutons; stochastic differential equations; universal phenomena; Liouville quantum gravity; SLE curves
Codes MSC : The main goal of the talk is to present a new family of universal limiting permutons, called skew Brownian permuton. This family includes (as particular cases) some already studied limiting permutons, such as the biased Brownian separable permuton and the Baxter permuton. We also show that some natural families of random constrained permutations converge to some new instances of the skew Brownian permuton.
The construction of these new limiting objects will lead us to investigate an intriguing connection with some perturbed versions of the Tanaka SDE and the SDEs encoding skew Brownian motions. We finally explain how it is possible to construct these new limiting permutons directly from a Liouville quantum gravity decorated with two SLE curves. Building on the latter connection, we compute the density of the intensity measure of the Baxter permuton.
Keywords : permutations; permutons; stochastic differential equations; universal phenomena; Liouville quantum gravity; SLE curves
60D05 - Geometric probability and stochastic geometry
60G57 - Random measures
60H10 - Stochastic ordinary differential equations
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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 arXiv category : Probability ; Mathematical Physics ; Combinatorics Domaine : Combinatorics ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:48:35 Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-17_Borga.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.19875703Citer cette vidéo: Borga, Jacopo (2022). The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19875703 URI : http://dx.doi.org/10.24350/CIRM.V.19875703 |
Voir aussi
- [Multi angle] Some questions on the Brownian Map motivated by its higher-genus analogues / Auteur de la Conférence Chapuy, Guillaume.
- [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] Geometry of the sign clusters in the Infinite Ising-weighted triangulation / Auteur de la Conférence Albenque, Marie.
Bibliographie
- BORGA, Jacopo. The skew Brownian permuton: a new universality class for random constrained permutations. arXiv preprint arXiv:2112.00156, 2021. - https://arxiv.org/abs/2112.00156
- BORGA, Jacopo. The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permuton. arXiv preprint arXiv:2112.00159, 2021. - https://arxiv.org/abs/2112.00159
- BORGA, Jacopo et MAAZOUN, Mickaël. Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes. arXiv preprint arXiv:2008.09086, 2020. - https://arxiv.org/abs/2008.09086
- BORGA J., HOLDEN N., SUN X., and YU P.. Baxter permuton and Liouville quantum gravity. Work in progress (2022+). -
- ANG, Morris, HOLDEN, Nina, et SUN, Xin. Conformal welding of quantum disks. arXiv preprint arXiv:2009.08389, 2020. - https://arxiv.org/abs/2009.08389
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