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Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2016

A quantitative central limit theorem for the effective conductance on the discrete torus

Résumé

We study a random conductance problem on a d-dimensional discrete torus of size L>0. The conductances are independent, identically distributed random variables uniformly bounded from above and below by positive constants. The effective conductance AL of the network is a random variable, depending on L, and the main result is a quantitative central limit theorem for this quantity as L→∞. In terms of scalings we prove that this nonlinear nonlocal function AL essentially behaves as if it were a simple spatial average of the conductances (up to logarithmic corrections). The main achievement of this contribution is the precise asymptotic description of the variance of AL.

Dates et versions

hal-01093352 , version 1 (10-12-2014)

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Antoine Gloria, James Nolen. A quantitative central limit theorem for the effective conductance on the discrete torus. Communications on Pure and Applied Mathematics, 2016, 69 (12), pp.2304--2348. ⟨10.1002/cpa.21614⟩. ⟨hal-01093352⟩
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