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When J. Ginibre met E. Schrödinger
Multi angle
Authors : Bothner, Thomas (Author of the conference)
CIRM (Publisher )
45M05 - Asymptotics
60B20 - Random matrices (probabilistic aspects)
60G70 - Extreme value theory; extremal processes
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Bothner.pdf
CIRM (Publisher )
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Abstract :
The real Ginibre ensemble consists of square real matrices whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble, real eigenvalues in the real Ginibre ensemble attain positive likelihood. In turn, the spectral radius of a real Ginibe matrix follows a different limiting law for purely real eigenvalues than for non-real ones. Building on previous work by Rider, Sinclair and Poplavskyi, Tribe, Zaboronski, we will show that the limiting distribution of the largest real eigenvalue admits a closed form expression in terms of a distinguished solution to an inverse scattering problem for the Zakharov-Shabat system. This system is directly related to several of the most interesting nonlinear evolution equations in 1+1 dimensions which are solvable by the inverse scattering method, for instance the nonlinear Schr¨odinger equation. The results of this talk are based on the recent preprint arXiv:1808.02419, joint with Jinho Baik.
MSC Codes : 45M05 - Asymptotics
60B20 - Random matrices (probabilistic aspects)
60G70 - Extreme value theory; extremal processes
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Bothner.pdf
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Information on the Video
Film maker : Recanzone, 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 ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:50:17 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-11_Bothner.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.19517103Cite this video as: Bothner, Thomas (2019). When J. Ginibre met E. Schrödinger. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19517103 URI : http://dx.doi.org/10.24350/CIRM.V.19517103 |
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Bibliography
- Baik, J., & Bothner, T. (2018). The largest real eigenvalue in the real Ginibre ensemble and its relation to the nonlinear Schrödinger equation. arXiv preprint arXiv:1808.02419. - arXiv:1808.02419v3
