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<p>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 <i>relevant limiting spectrum</i>, we describe the connection between these two sets.</p>

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High-Contrast Random Composites: Homogenisation Framework and Spectral Convergence

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月2日

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  • Mikhail Cherdantsev,
  • Kirill Cherednichenko,
  • Igor Velčić

摘要

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.