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The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity
Multi angle
Authors : Borga, Jacopo (Author of the conference)
CIRM (Publisher )
60D05 - Geometric probability and stochastic geometry
60G57 - Random measures
60H10 - Stochastic ordinary differential equations
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/02/2022 Conference Date : 17/01/2022 Subseries : Research talks arXiv category : Probability ; Mathematical Physics ; Combinatorics Mathematical Area(s) : Combinatorics ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:48:35 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-17_Borga.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.19875703Cite this video as: 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 |
See Also
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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.
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Bibliography
- 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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