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SUMMARY:Transport of Gaussian measures under Hamiltonian and stochastic dy
 namics.
DTSTART:20260116T083000
DTEND:20260116T091000
DTSTAMP:20260416T053139Z
UID:abd2f2430fd27bdfcdaa124076dc4a3df5800a18828f71133ff2dacd
CATEGORIES:Conferences - Seminars
DESCRIPTION:James Coe \nWe consider the evolution of Gaussian measures un
 der infinite-dimensional dynamics\, in both Hamiltonian and dissipative se
 ttings.\n\nIn the Hamiltonian case\, we consider the flow of Gaussian meas
 ures under the Szego equation\, a toy model for weakly-dispersive systems.
  We identify a sharp transition between quasi-invariance of measures above
  a certain regularity and a singular regime below\, where the laws of solu
 tions are immediately singular with respect to the initial distribution. T
 hese regimes are determined by the instantaneous change in the energy prof
 ile of solutions.\n\nIn the dissipative case\, we consider the 2d incompre
 ssible Navier--Stokes equations with Gaussian forcing that is white-in-tim
 e and coloured-in-space. Using a nonlinear time-shifted Girsanov method\, 
 we show that the time marginals of solutions are equivalent to those of th
 e associated Ornstein--Uhlenbeck process. We exploit the skew-symmetric st
 ructure of the Navier--Stokes nonlinearity to construct a modified system 
 that leaves the Gaussian measure invariant while remaining comparable to t
 he Navier--Stokes dynamics.\n\nThis talk is based on joint work with Marti
 n Hairer and Leonardo Tolomeo.
LOCATION:Bernoulli Center - GA 3 21 https://plan.epfl.ch/?room==GA%203%202
 1
STATUS:CONFIRMED
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