An informal introduction to quantitative stochastic homogenization

Abstract

Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review one approach for doing so based on the idea of renormalization. The discussion is highly informal, with pointers to mathematically precise statements.

18 pages, 9 figures, proceedings of ICMP 2018

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Cited by in corpus (2)

• Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids
• Uniform estimate of an iterative method for elliptic problems with rapidly oscillating coefficients