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SUMMARY:Perturbation\, Noise\, and Averaged Dynamics - Xue-Mei Li (Imperia
 l College London)
DTSTART:20190502T102500Z
DTEND:20190502T111000Z
UID:TALK123895@talks.cam.ac.uk
CONTACT:Ferdia Sherry
DESCRIPTION:Perturbation and approximation underly almost all applications
  of physical mathematical models. The averaging method\, first introduced 
 for approximate periodic motions\, is now widely used for a large class of
  problems in both pure and applied mathematics.\nThe purpose of averaging 
 is easy to describe. Suppose that we have a system of variables interactin
 g with each other and moving at different scales of speed (of order 1 and 
 of order 1/epsilon) with the fast variables `fast oscillatory’. Both slo
 w and fast variables evolve in time according to some rules\, for example 
 solving a family of differential or stochastic differential equations. The
  aim is to determine whether the slow variables can be approximated by an 
 autonomous systems of equations\, called the effective dynamic\, as epsilo
 n is taken to 0 and the speed of the fast variables tends to infinity. Slo
 w/fast systems arise from perturbations of conservation laws and breaking 
 of symmetries.\nWe will discuss the latest developments in averaged dynami
 cs\, touching on recent work with M. Hairer on averaged dynamics with frac
 tional noise (this leads to very different behaviour from the white noise 
 case and requires new techniques).
LOCATION:Centre for Mathematical Sciences\, MR2
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