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arXiv · 2104.09416

Eigenvalue fluctuations for random elliptic operators in homogenization regime

Mitia Duerinckx
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Abstract

This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for isolated eigenvalues towards eigenvalues of the homogenized problem, as well as a quantitative two-scale expansion result for eigenfunctions. Next, a quantitative central limit theorem is established for eigenvalue fluctuations; more precisely, a pathwise characterization of eigenvalue fluctuations is obtained in terms of the so-called homogenization commutator, in parallel with the recent fluctuation theory for the solution operator.

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Mitia Duerinckx. 2021-04-19. Eigenvalue fluctuations for random elliptic operators in homogenization regime. https://doi.org/10.1007/s10955-022-02918-2

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