Work

Green function and invariant measure estimates for nondivergence form elliptic homogenization

Year: 2022

Type: preprint

Abstract: We prove quantitative estimates on the the parabolic Green function and the stationary invariant measure in the context of stochasic homogenization of elliptic equations in nondivergence form. We consequently obtain a quenched, local CLT for the corresponding diffusion process and a quantitative ergodicity estimate for the environmental process. Each of these results are characterized by deterministic (in terms of the environment) estimates which are valid above a random, ``minimal'' length scale, the stochastic moments of which we estimate sharply.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2211.13279

Authors: Armstrong, Scott, Fehrman, Benjamin, Lin, Jessica

Institutions: Courant Institute of Mathematical Sciences, Sorbonne Université, Laboratoire Jacques-Louis Lions, New York University, Louisiana State University, McGill University

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, European Commission, Canada Research Chairs, HORIZON EUROPE Framework Programme, Natural Sciences and Engineering Research Council of Canada, Engineering and Physical Sciences Research Council

Awards: Random environments, stochastic equations, and randomized algorithms, Fluctuating systems, random environments, and stochastic algorithms, Quantitative Stochastic Homogenization and Renormalization Methods, Renormalization in Statistical Mechanics and Partial Differential Equations, Coarse-graining, Renormalization, and Fractal Homogenization

OpenAlex ID: W4310266207

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Cited by: 1

Related to: 10