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.
Mots-Clés : 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.
Mots-Clés : 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 Catégorie arXiv : Probability ; Mathematical Physics ; Combinatorics Domaine(s) : Combinatoires ; Physique Mathématique ; Probabilités & Statistiques Format : MP4 (.mp4) - HD Durée : 00:48:35 Audience : Chercheurs 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 de la Rencontre : 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 |
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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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