Submean variance bound for effective resistance on random electric networks
نویسنده
چکیده
Abstract : We study a model of random electric networks with Bernoulli resistances. In the case of the lattice Z, we show that the point-to-point effective resistance has a small variance compared to its expected value, whereas for Z, d 6= 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 Poincaré inequality due to Falik and Samorodnitsky [7].
منابع مشابه
Submean variance bound for effective resistance of random electric networks
Abstract : We study a model of random electric networks with Bernoulli resistances. In the case of the lattice Z, we show that the point-to-point effective resistance between 0 and a vertex v has a variance of order at most (log |v|) 23 whereas its expected value is of order log |v|, when v goes to infinity. When d 6= 2, expectation and variance are of the same order. Similar results are obtain...
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