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Log-gases on a quadratic lattice via discrete loop equations
Multi angle
Authors : Knizel, Alisa (Author of the conference)
CIRM (Publisher )
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
82C22 - Interacting particle systems
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Knizel.pdf
CIRM (Publisher )
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Abstract :
We study a general class of log-gas ensembles on a quadratic lattice. Using a variational principle we prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance.
We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field.
Our approach is based on a q-analogue of the Schwinger-Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to a quadratic lattice.
Based on joint work with Evgeni Dimitrov
Keywords : log-gases; loop equation
MSC Codes : We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field.
Our approach is based on a q-analogue of the Schwinger-Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to a quadratic lattice.
Based on joint work with Evgeni Dimitrov
Keywords : log-gases; loop equation
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
82C22 - Interacting particle systems
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Knizel.pdf
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 09/05/2019 Conference Date : 11/04/2019 Subseries : Research talks arXiv category : Probability ; Mathematical Physics Mathematical Area(s) : Mathematical Physics ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:49:43 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-11_Knizel.mp4 
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Information on the Event
Event Title : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial DataEvent Organizers : Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken Dates : 08/04/2019 - 12/04/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2104.html
Citation Data
DOI : 10.24350/CIRM.V.19516703Cite this video as: Knizel, Alisa (2019). Log-gases on a quadratic lattice via discrete loop equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19516703 URI : http://dx.doi.org/10.24350/CIRM.V.19516703 |
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Bibliography
- Dimitrov, Evgeni; Knizel, Alisa - Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions. J. Funct. Anal. 276, No. 10, 3067-3169 (2019). - https://doi.org/10.1016/j.jfa.2018.12.008
