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Multicritical Schur measures

De Jérémie Bouttier

Apparaît dans la collection : Random Geometry / Géométrie aléatoire

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.

Informations sur la vidéo

Date de captation 18/01/2022
Date de publication 04/02/2022
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19877203
Citer cette vidéo Bouttier, Jérémie (18/01/2022). Multicritical Schur measures. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19877203
URL https://dx.doi.org/10.24350/CIRM.V.19877203

Domaine(s)

Bibliographie

BETEA, Dan, BOUTTIER, Jérémie, et WALSH, Harriet. Multicritical random partitions. arXiv preprint arXiv:2012.01995, 2020. - https://arxiv.org/abs/2012.01995

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/2528/Slides/bouttier.pdf

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