Submean variance bound for effective resistance of random electric networks

Details Submean variance bound for effective resistance of random electric networks Submean variance bound for effective resistance of random electric networks

2006-10-12

arxiv.org/abs/math/0610393v4

Mathematics

Probability

Final version, to appear in CMP (minor changes compared to version 3)

Scientific paper

We study a model of random electric networks with Bernoulli resistances. In the case of the lattice Z^2, we show that the point-to-point effective resistance between 0 and a vertex v has a variance of order at most (log |v|)^(2/3) whereas its expected value is of order log |v|, when v goes to infinity. When the dimension of Z^d is different than 2, expectation and variance are of the same order. Similar results are obtained in the context of p-resistance. The proofs rely on a modified Poincare inequality due to Falik and Samorodnitsky.

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