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Noise-stability and central limit theorems for effective resistance of random electric networks. (English) Zbl 1347.60133

This long article deals with the generalized Walsh decomposition (or Efron-Stein decomposition) of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. The main purpose of this paper is indeed to derive the right order of the variances of the effective resistance (and the effective conductivity) and to improve the understanding of their fluctuations by deriving Gaussian central limit theorems for these quantities in the context of the \(d\)-dimensional torus.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
60K99 Special processes
05C21 Flows in graphs
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