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SUMMARY:Path large deviations for kinetic theories: beyond the Boltzmann\,
  the Landau\, the Balescu—Lenard—Guernsey\, and the weak turbulence ki
 netic equations + Rare event dynamics applied to climate models -  Freddy 
 Bouchet\, ENS Paris
DTSTART:20230207T130000Z
DTEND:20230207T140000Z
UID:TALK193459@talks.cam.ac.uk
CONTACT:Camille Scalliet
DESCRIPTION:Online seminar \n\nIn many physical systems one seeks to descr
 ibe effectively mesoscopic or macroscopic variables. Kinetic theories and 
 kinetic equations are examples where the average mesoscopic dynamics is ob
 tained through very clear theoretical procedures and can possibly lead to 
 mathematical proofs\, for instance the Boltzmann equation for dilute gases
 \, the Landau or the Balescu—Guernsey—Lenard equations in plasma physi
 cs\, or the wave kinetic equation for weak turbulence theory. A few works 
 go beyond the average evolution and describe\, for instance\, Gaussian flu
 ctuations. However\, for many physical systems\, rare events can be of imp
 ortance\, and Gaussian fluctuations are not relevant. This is the case for
  instance if one wants to understand the irreversibility paradox associate
 d to the kinetic equations\, or to understand the dynamics that leads to r
 are events with big impact. \nThe aim of this presentation is to describe 
 recent results where we derived explicitly the functional that describes t
 he path large deviations for the empirical measure of dilute gases\, plasm
 a\, systems of particles with long range interactions\, and waves with wea
 k interactions. The associated kinetic equations (the average evolution) a
 re then either the Boltzmann\, the Landau\, the Balescu--Lenard—Guernsey
 \, or the weak turbulence kinetic equations.  After making the classic ass
 umptions in theoretical physics textbooks for deriving the kinetic equatio
 n\, our derivation of the large deviation functional is exact.\nThese path
  large deviation principles give a very nice and transparent new interpret
 ation of the classical irreversibility paradox. This new explanation is fu
 lly compatible with the classical one\, but it gives a deeper insight.\nAl
 though this will not be the subject of this talk\, I will take five to ten
  minutes to review our current work to apply rare event algorithms for stu
 dying climate extreme events and abrupt transitions.\n\nJoint works with G
 regory Eyink\, Ouassim Feliachi\, Jules Guioth and Yohei Onuki\n \nReferen
 ces:\nFor the large deviations associated to the Boltzmann equation (dilut
 e gazes)\, and a general introduction (published in J. Stat. Phys. in 2020
 ): F. Bouchet\, 2020\, Journal of Statistical Physics\, 181\, 515–550.\n
  \nFor the large deviations associated to the Landau equation (plasma belo
 w the Debye length\, accepted for publication in J. Stat. Phys. in March 2
 021): O. Feliachi and F. Bouchet\, 2021\, Journal of Statistical Physics\,
  183\, 42.\n\nFor the large deviations associated with the Balescu—Guern
 sey--Lenard equation (plasma and systems with long range interactions): O.
  Feliachi and F. Bouchet\, 2022\, Journal of Statistical Physics 186\, 22\
 , and arxiv:2105.05644\n \nFor the large deviations associated with the we
 ak turbulence kinetic equation that describe weakly interacting waves: J. 
 Guioth\, F. Bouchet and G. L. Eyink\, 2022\, J Stat Phys\, 189\, 20 \, arX
 iv:2203.11737.\n\nFor the large deviations associated with the weak turbul
 ence kinetic equation that describe weakly interacting waves in heterogene
 ous versions: Y. Onuki\, J. Guioth\, and F. Bouchet\, 2023\, arXiv:2301.03
 257.
LOCATION:https://maths-cam-ac-uk.zoom.us/j/98016675669\, screened in Cente
 r for Mathematical Sciences MR4
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