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High-contrast random composites: homogenisation framework and new spectral phenomena

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arxiv 2110.00395 v5 pith:OAQM3GTQ submitted 2021-10-01 math.AP math.SP

classification math.APmath.SP
keywords high-contrastoperatorsrandomanalysisframeworkhomogenisedlimitoperator
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We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator. Under some lenient assumptions on the configuration of the random inclusions, we fully characterise the limit of the spectra of the high-contrast operators in question, which unlike in the periodic setting is shown to be different to the spectrum of the homogenised operator. Introducing a new notion of the relevant limiting spectrum, we describe the connection between these two sets.

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Cited by 2 Pith papers

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

  1. Homogenisation and spectral convergence of high-contrast convolution type operators

    math.AP 2025-07 conditional novelty 7.0 of 10

    The limiting spectrum of high-contrast convolution-type operators is characterized via a beta function and generally contains extra contributions beyond the two-scale limit operator's spectrum.

  2. Quantitative estimates for high-contrast random media

    math.AP 2025-02 conditional novelty 6.0 of 10

    For elliptic equations with random well-separated holes, the paper proves stretched-exponential tails for the regularity radius and sublinear corrector growth under a multiscale spectral gap condition.

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