High-contrast random composites: homogenisation framework and spectral convergence

Cherdantsev, Mikhail ORCID: https://orcid.org/0000-0002-5175-5767, Cherednichenko, Kirill and Velčić, Igor 2026. High-contrast random composites: homogenisation framework and spectral convergence. Communications in Mathematical Physics 407 (6) , 113. 10.1007/s00220-026-05601-9

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Abstract

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.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/, Type: open-access
Publisher:	Springer
ISSN:	0010-3616
Funders:	EPSRC
Projects:	EP/L018802/2; EP/V013025/1
Date of First Compliant Deposit:	6 May 2026
Date of Acceptance:	24 February 2026
Last Modified:	10 Jun 2026 13:52
URI:	https://orca.cardiff.ac.uk/id/eprint/186823

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