Titlebook: Quantitative Stochastic Homogenization and Large-Scale Regularity; Scott Armstrong,Tuomo Kuusi,Jean-Christophe Mourra Book 2019 Springer N

staging

https://doi.org/10.1007/978-3-030-15545-2stochastic homogenization; large-scale regularity theory; optimal error estimates; Gaussian free field;

良心

Introduction and Qualitative Theory,a soft argument, based on the convergence of a certain subadditive quantity we call .. We demonstrate that a quantitative homogenization result for general Dirichlet problems can be reduced to an estimate on the rate of convergence of . to its limit.

FER

腐蚀

CIS

Quantitative Description of First-Order Correctors,ument is based on a renormalization of energy quantities: using the large-scale regularity estimates as the new ingredient, we show that, as we pass to larger and larger scales, the energy densities of the correctors behave like a white noise field.

Ascendancy

BRAND

LUMEN

裂隙

Convergence of the Subadditive Quantities, based on the interplay between . and a new “dual” subadditive quantity .. We show, by an iteration of the scales, that these quantities are becoming close to convex dual functions, up to an error which is a negative power of the length scale.

Ptsd429