|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 Clement 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 listsResearch Group of Centre of Governance and Human Rights Combinatorics Seminar CJCR
Other talksC++11: The new C++ Natural Killer cells and their function against virus-infected cells Validity unpacked All about bees, flowers, pollination and electric fields Dynamics of Elastic Capsules in Flow The Paradox of Parallel Lives; Immigration Policy and Transnational Polygyny between Senegal and France