Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

• 成果类型: Article
• 署名作者: Mourrat, Jean-Christophe
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0529-5
• 发表日期: 2014
• 页码: 279-314
• 关键词: reversible markov-processes; central-limit-theorem; heat-kernel decay; harnack inequality; CONVERGENCE; percolation; diffusion; discrete; rates; walks

摘要

The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For smooth initial condition, the rescaled solution of such an equation, once averaged over the randomness, is shown to converge polynomially fast to the solution of the homogenized equation, with an explicit exponent depending only on the dimension. Polynomial rate of homogenization for the averaged heat kernel, with an explicit exponent, is then derived. Similar results for elliptic equations are also presented.