Submean variance bound for effective resistance of random electric networks
| dc.creator | Benjamini, Itai | |
| dc.creator | Rossignol, Raphael | |
| dc.date | 2006-10-12 | |
| dc.date | 2007-11-28 | |
| dc.date.accessioned | 2026-07-07T08:45:29Z | |
| dc.date.available | 2026-07-07T08:45:29Z | |
| dc.description | 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. | |
| dc.description | Final version, to appear in CMP (minor changes compared to version 3) | |
| dc.identifier | https://arxiv.org/abs/math/0610393 | |
| dc.identifier | http://arxiv.org/abs/math/0610393 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142979 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | Primary 60E15; secondary 31C20, 31A99, 31C45 | |
| dc.title | Submean variance bound for effective resistance of random electric networks | |
| dc.type | text |