Submean Variance Bound for Effective Resistance of Random Electric Networks
نویسندگان
چکیده
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...
متن کاملSubmean variance bound for effective resistance on 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 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 inequa...
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∗Copyright (C) 1999, 2000, 2006 Peter G. Doyle and J. Laurie Snell. Derived from their Carus Monograph, Copyright (C) 1984 The Mathematical Association of America. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, as published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2008
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-008-0476-7