QUANTITATIVE HOMOGENIZATION OF THE DISORDERED ∇φ MODEL
Paul Dario · HAL (Le Centre pour la Communication Scientifique Directe) · 2019
We study the discrete Ginzburg-Landau model with uniformly convex Hamiltonian and prove a quantitative rate of convergence for the properly rescaled partition function as well as a quantitative rate of convergence for the field φ subject to affine boundary condition in the L 2 norms. One of our motivations is to develop a new toolbox for studying this problem that does not rely on the Helffer-Sjöstrand representation. Instead, we make use of the variational formulation of the partition function, the notion of displacement convexity from the theory of optimal transport, and the recently developed theory of quantitative stochastic homogenization.