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SUMMARY:Quantitative estimates in stochastic homogenization - Daniel Marah
 rens (Max-Planck-Institute\, Leipzig)
DTSTART:20130213T150000Z
DTEND:20130213T160000Z
UID:TALK43268@talks.cam.ac.uk
CONTACT:Prof. Clément Mouhot
DESCRIPTION:Consider a discrete elliptic equation on the integer lattice w
 ith random coefficients\, arising for example as the steady state of a dif
 fusion through the lattice with random diffusivities. Classical homogeniza
 tion results show that with ergodic coefficients and on large scales\, the
  solutions behave as the solutions to a diffusion equation with constant h
 omogenized coefficients. The homogenized coefficients can be characterised
  through the solution to a so-called "corrector problem". In contrast to p
 eriodic homogenization\, the stochastic homogenization lacks compactness w
 hich makes the problem harder. Recently Gloria\, Otto and Neukamm have dev
 eloped tools to obtain optimal estimates for the homogenization and the co
 rrector problem via a spectral gap inequality. In this talk\, I will prese
 nt how to obtain strong quantitative (optimal) estimates on the discrete G
 reen's function via a logarithmic Sobolev inequality and consequences from
  these estimates for the solutions to the discrete equation. This is joint
  work with Felix Otto.
LOCATION:CMS\, MR11
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