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Random triangulations and bijective paths to Liouville quantum gravity
Virtualconference
Authors : Holden, Nina (Author of the conference)
CIRM (Publisher )
05A19 - Combinatorial identities, bijective combinatorics
60C05 - Combinatorial probability
60D05 - Geometric probability and stochastic geometry
60F17 - Functional limit theorems; invariance principles
60G60 - Random fields
60J67 - Stochastic (Schramm-)Loewner evolution (SLE)
Additional resources :
https://www.cirm-math.fr/RepOrga/2324/Slides/slides_holden.pdf
CIRM (Publisher )
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Abstract :
Planar maps are planar graphs embedded in the sphere viewed modulo continuous deformations. There are two families of bijections between planar maps and lattice paths that are applied to prove scaling limit results of planar maps to so-called Liouville quantum gravity surfaces: metric bijections and mating-of-trees bijections. We will present scaling limit results obtained in this way, including works with Bernardi and Sun and with Albenque and Sun.
Keywords : Liouville quantum gravity; chramm-Loewner evolutions; mating of trees; percolation; random planar maps; triangulations; random walks; Kreweras walks; planar Brownian motion; bijection
MSC Codes : Keywords : Liouville quantum gravity; chramm-Loewner evolutions; mating of trees; percolation; random planar maps; triangulations; random walks; Kreweras walks; planar Brownian motion; bijection
05A19 - Combinatorial identities, bijective combinatorics
60C05 - Combinatorial probability
60D05 - Geometric probability and stochastic geometry
60F17 - Functional limit theorems; invariance principles
60G60 - Random fields
60J67 - Stochastic (Schramm-)Loewner evolution (SLE)
Additional resources :
https://www.cirm-math.fr/RepOrga/2324/Slides/slides_holden.pdf
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 02/08/2021 Conference Date : 22/06/2021 Subseries : Research talks arXiv category : Probability ; Mathematical Physics ; Combinatorics Mathematical Area(s) : Combinatorics ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:59:23 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-06-22_Holden.mp4 
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Information on the Event
Event Title : Lattice Paths, Combinatorics and Interactions / Marches aléatoires, combinatoire et interactionsEvent Organizers : Banderier, Cyril ; Dousse, Jehanne ; Duchi, Enrica ; Krattenthaler, Christian ; Wallner, Michael Dates : 21/06/2021 - 25/06/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2324.html
Citation Data
DOI : 10.24350/CIRM.V.19769903Cite this video as: Holden, Nina (2021). Random triangulations and bijective paths to Liouville quantum gravity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19769903 URI : http://dx.doi.org/10.24350/CIRM.V.19769903 |
See Also
- [Virtualconference] Using symbolic dynamical programming in lattice paths combinatorics / Author of the conference Zeilberger, Doron.
- [Virtualconference] The alternating sign matrices and descending plane partitions : n+3 pairs of equivalent statistics / Author of the conference Fischer, Ilse.
- [Multi angle] Lattice paths and heaps / Author of the conference Viennot, Xavier.
- [Multi angle] Mating of discrete trees and walks in the quarter plane / Author of the conference Biane, Philippe.
- [Virtualconference] Bijections between walks inside a triangular domain and Motzkin paths of bounded amplitude / Author of the conference Marcovici, Irène.
Bibliography
- BERNARDI, Olivier, HOLDEN, Nina, et SUN, Xin. Percolation on triangulations: a bijective path to Liouville quantum gravity. ArXiv e-prints, 2018. (To appear in Memoirs of the American Mathematical Society) - https://arxiv.org/abs/1807.01684
- ALBENQUE, Marie, HOLDEN, Nina, SUN, Xin, et al. Scaling limit of triangulations of polygons. Electronic Journal of Probability, 2020, vol. 25. - http://dx.doi.org/10.1214/20-EJP537
