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Nonbijective scaling limit of maps via restriction
Multi angle
Authors : Bettinelli, Jérémie (Author of the conference)
CIRM (Publisher )
60C05 - Combinatorial probability
60F17 - Functional limit theorems; invariance principles
Additional resources :
https://www.cirm-math.fr/RepOrga/2528/Slides/XX_restrict_beam.pdf
CIRM (Publisher )
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Abstract :
The main purpose of this work is to provide a framework for proving that, given a family of random maps known to converge in the Gromov--Hausdorff sense, then some (suitable) conditional families of random maps converge to the same limit. As a proof of concept, we show that quadrangulations with a simple boundary converge to the Brownian disk. More precisely, we fix a sequence $(p_n)$ of even positive integers with $p_n\sim2\alpha \sqrt{2n}$ for some $\alpha\in(0,\infty)$. Then, for the Gromov--Hausdorff topology, a quadrangulation with a simple boundary uniformly sampled among those with $n$ inner faces and boundary length $p_n$ weakly converges, in the usual scaling $n^{-1/4}$, toward the Brownian disk of perimeter $3\alpha$.
Keywords : maps; Brownian disk; Gromov-Hausdorff
MSC Codes : Keywords : maps; Brownian disk; Gromov-Hausdorff
60C05 - Combinatorial probability
60F17 - Functional limit theorems; invariance principles
Additional resources :
https://www.cirm-math.fr/RepOrga/2528/Slides/XX_restrict_beam.pdf
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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 Area(s) : Combinatorics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:56:03 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-17_Bettinelli.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.19875903Cite this video as: Bettinelli, Jérémie (2022). Nonbijective scaling limit of maps via restriction. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19875903 URI : http://dx.doi.org/10.24350/CIRM.V.19875903 |
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Bibliography
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