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Correlation functions for some integrable systems with random initial data, theory and computation - Lecture 1
Multi angle
Authors : Grava, Tamara (Author of the conference)
CIRM (Publisher )
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
60B20 - Random matrices (probabilistic aspects)
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
CIRM (Publisher )
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Abstract :
We will investigate the form of spatio-temporal correlation functions for integrable models of systems of particles on the line. There are few analytical results for nonlinear systems, and so we start developing intuition from harmonic chains, where steepest descent analysis yields detailed asymptotic behaviour of the correlation functions in a variety of scaling limits. We will introduce integrable nonlinear lattices, explain the integrable solution procedure, as well as computational simulations to see dynamics of correlation functions in action.
MSC Codes : 37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
60B20 - Random matrices (probabilistic aspects)
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/03/2019 Conference Date : 14/03/2019 Subseries : Research School arXiv category : Probability ; Spectral Theory ; Mathematical Physics Mathematical Area(s) : Dynamical Systems & ODE ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:42:23 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2019-03-14_Grava.mp4 
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Information on the Event
Event Title : Jean-Morlet chair - Research school: Coulomb gas, integrability and Painlevé equations / Chaire Jean-Morlet - École de recherche : Gaz de Coulomb, intégrabilité et équations de PainlevéEvent Organizers : Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara Dates : 11/03/2019 - 15/03/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2105.html
Citation Data
DOI : 10.24350/CIRM.V.19503103Cite this video as: Grava, Tamara (2019). Correlation functions for some integrable systems with random initial data, theory and computation - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19503103 URI : http://dx.doi.org/10.24350/CIRM.V.19503103 |
See Also
- [Multi angle] Operator limits of beta ensembles - Lecture 4 / Author of the conference Rider, Brian.
- [Multi angle] Random matrices, integrability, and number theory - Lecture 4 / Author of the conference Keating, Jonathan P..
- [Multi angle] Toeplitz determinants, Painlevé equations, and special functions. Part II: a Riemann-Hilbert point of view - Lecture 2 / Author of the conference Its, Alexander R..
- [Multi angle] Operator limits of beta ensembles - Lecture 3 / Author of the conference Rider, Brian.
- [Multi angle] Operator limits of beta ensembles - Lecture 2 / Author of the conference Rider, Brian.
- [Multi angle] Operator limits of beta ensembles - Lecture 1 / Author of the conference Rider, Brian.
- [Multi angle] Random matrices, integrability, and number theory - Lecture 3 / Author of the conference Keating, Jonathan P..
- [Multi angle] Random matrices, integrability, and number theory - Lecture 2 / Author of the conference Keating, Jonathan P..
- [Multi angle] Random matrices, integrability, and number theory - Lecture 1 / Author of the conference Keating, Jonathan P..
- [Multi angle] Toeplitz determinants, Painlevé equations, and special functions. Part II: a Riemann-Hilbert point of view - Lecture 3 / Author of the conference Its, Alexander R..
- [Multi angle] Toeplitz determinants, Painlevé equations, and special functions. Part II: a Riemann-Hilbert point of view - Lecture 1 / Author of the conference Its, Alexander R..
- [Multi angle] Correlation functions for some integrable systems with random initial data, theory and computation - Lecture 2 / Author of the conference McLaughlin, Kenneth D. T.-R..
- [Multi angle] Determinantal point processes - Lecture 3 / Author of the conference Bufetov, Alexander.
- [Multi angle] Determinantal point processes - Lecture 2 / Author of the conference Bufetov, Alexander.
- [Multi angle] Determinantal point processes - Lecture 1 / Author of the conference Bufetov, Alexander.
- [Multi angle] Toeplitz determinants, Painlevé equations, and special functions. Part I: an operator approach - Lecture 3 / Author of the conference Basor, Estelle.
- [Multi angle] Toeplitz determinants, Painlevé equations, and special functions. Part I: an operator approach - Lecture 2 / Author of the conference Basor, Estelle.
- [Multi angle] Toeplitz determinants, Painlevé equations, and special functions. Part I: an operator approach - Lecture 1 / Author of the conference Basor, Estelle.
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