|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Quantitative estimates in stochastic homogenization
If you have a question about this talk, please contact Prof. Clément Mouhot.
Consider a discrete elliptic equation on the integer lattice with random coefficients, arising for example as the steady state of a diffusion through the lattice with random diffusivities. Classical homogenization results show that with ergodic coefficients and on large scales, the solutions behave as the solutions to a diffusion equation with constant homogenized coefficients. The homogenized coefficients can be characterised through the solution to a so-called “corrector problem”. In contrast to periodic homogenization, the stochastic homogenization lacks compactness which makes the problem harder. Recently Gloria, Otto and Neukamm have developed tools to obtain optimal estimates for the homogenization and the corrector problem via a spectral gap inequality. In this talk, I will present how to obtain strong quantitative (optimal) estimates on the discrete Green’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.
This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsEuropean Bioinformatics Institute Cambridge Climate and Sustainability Forum Cambridge Neuroscience Seminar, 2011
Other talksEmerging Diseases: The Culture of Viruses Flexural Mechanics of Subduction Webinars for Professional Development in the Arts Series 11: Music Therapy in Education Gareth Stedman Jones: Karl Marx and American Politics - The New York Tribune Years CGHR Research Group Cellulose Photonics: from nature to applications