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Quantitative Stochastic Homogenization and Large-Scale Regularity

  • Scott Armstrong
  • Tuomo Kuusi
  • Jean-Christophe Mourrat
Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 352)

Table of contents

  1. Front Matter
    Pages i-xxxviii
  2. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 1-35
  3. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 37-66
  4. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 67-121
  5. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 123-190
  6. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 191-242
  7. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 243-274
  8. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 275-299
  9. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 301-346
  10. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 347-390
  11. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 391-415
  12. Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
    Pages 417-454
  13. Back Matter
    Pages 455-518

About this book

Introduction

The focus of this book is the large-scale statistical behavior of solutions of divergence-form elliptic equations with random coefficients, which is closely related to the long-time asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature. 


Keywords

stochastic homogenization large-scale regularity theory optimal error estimates Gaussian free field rates of convergence two-scale expansion calculus of variations 35B27, 60F17, 35B65 renormalization random walk in random environment random conductance model divergence-form elliptic equation invariance principle Green function

Authors and affiliations

  • Scott Armstrong
    • 1
  • Tuomo Kuusi
    • 2
  • Jean-Christophe Mourrat
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew YorkUSA
  2. 2.The Department of Mathematics and Statistics, Faculty of ScienceUniversity of HelsinkiHelsinkiFinland
  3. 3.Département de MathématiquesÉcole Normale SupérieureParisFrance

Bibliographic information

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