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Multicritical Schur measures
Multi angle
Authors : Bouttier, Jérémie (Author of the conference)
CIRM (Publisher )
05A17 - Partitions of integers (combinatorics)
60B20 - Random matrices (probabilistic aspects)
60G55 - Point processes
Additional resources :
https://www.cirm-math.fr/RepOrga/2528/Slides/bouttier.pdf
CIRM (Publisher )
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Abstract :
Schur measures are random integer partitions, that map to determinantal point processes. We explain how to construct such measures whose edge behavior (asymptotic distribution of the largest parts) is governed by a higher-order analogue of the Airy ensemble/Tracy-Widom GUE distribution. This 'multicritical' analogue was previously encountered in models of fermions in non-harmonic traps, considered by Le Doussal, Majumdar and Schehr. These authors noted a coincidental connection with unitary random matrix models, which our construction explains via an exact mapping. This part is based on joint work with Dan Betea and Harriet Walsh.
If time allows, I will hint at a possible generalization that would correspond to a unitary analogue of the Ambjørn-Budd-Makeenko hermitian one-matrix model. This is work in progress.
Keywords : random partitions; Schur measures; random matrices
MSC Codes : If time allows, I will hint at a possible generalization that would correspond to a unitary analogue of the Ambjørn-Budd-Makeenko hermitian one-matrix model. This is work in progress.
Keywords : random partitions; Schur measures; random matrices
05A17 - Partitions of integers (combinatorics)
60B20 - Random matrices (probabilistic aspects)
60G55 - Point processes
Additional resources :
https://www.cirm-math.fr/RepOrga/2528/Slides/bouttier.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/02/2022 Conference Date : 18/01/2022 Subseries : Research talks arXiv category : Combinatorics ; Probability ; Mathematical Physics Mathematical Area(s) : Combinatorics ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 01:02:06 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-18_Bouttier.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.19877203Cite this video as: Bouttier, Jérémie (2022). Multicritical Schur measures. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19877203 URI : http://dx.doi.org/10.24350/CIRM.V.19877203 |
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Bibliography
- BETEA, Dan, BOUTTIER, Jérémie, et WALSH, Harriet. Multicritical random partitions. arXiv preprint arXiv:2012.01995, 2020. - https://arxiv.org/abs/2012.01995
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