Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analyticity of homogenized coefficients under Bernoulli perturbations
  and the Clausius-Mossotti formulas   This paper is concerned with the behavior of the homogenized coefficients
associated with some random stationary ergodic medium under a Bernoulli
perturbation. Introducing a new family of energy estimates that combine
probability and physical spaces, we prove the analyticity of the perturbed
homogenized coefficients with respect to the Bernoulli parameter. Our approach
holds under the minimal assumptions of stationarity and ergodicity, both in the
scalar and vector cases, and gives analytical formulas for each derivative that
essentially coincide with the so-called cluster expansion used by physicists.
In particular, the first term yields the celebrated (electric and elastic)
Clausius-Mossotti formulas for isotropic spherical random inclusions in an
isotropic reference medium. This work constitutes the first general proof of
these formulas in the case of random inclusions.

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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph