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Elliptic homogenization from qualitative to quantitative

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arxiv 2210.06488 v2 pith:5PGBNVSC submitted 2022-10-12 math.AP math.PR

Scott Armstrong , Tuomo Kuusi This is my paper · ORCID
classification math.APmath.PR
keywords fieldshomogenizationcoefficientellipticqualitativerandomclassicalcontains
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We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation also contains new results, such as optimal estimates (both in terms of stochastic moments and scaling of the error) for coefficient fields which are local functions of Gaussian random fields.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The diffusivity of supercritical Bernoulli percolation is infinitely differentiable

    math.PR 2025-06 conditional novelty 8.0 of 10

    The mapping p to sigma(p) for supercritical bond percolation on Z^d is C^infinity on (p_c,1], a full-interval extension of Kozlov's 1989 result.

  2. High-order Regularity Theory for High-contrast Elliptic Homogenization

    math.AP 2025-10 reject novelty 7.0 of 10

    High-order (C^{k,1}) large-scale regularity is established for high-contrast stochastic elliptic homogenization, along with a non-iterative Caccioppoli inequality.

  3. Parallel spin wave for the Villain model

    math.PR 2025-07 conditional novelty 7.0 of 10

    In three dimensions, the low-temperature Villain model's cosine-cosine correlation lies between c/|x|^2 and C(ln|x|)^{22}/|x|^2, matching the spin-wave prediction up to a logarithm; in all d at least 3 the upper bound...

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