Fulltext

Submean Variance Bound for Effective Resistance of Random Electric Networks

Benjamini, Itai ; Rossignol, Raphaël

In: Communications in Mathematical Physics, 2008, vol. 280, no. 2, p. 445-462

Ajouter à la liste personnelle
    Titre
    • Submean Variance Bound for Effective Resistance of Random Electric Networks
    Auteur
    • Benjamini, Itai. The Weizmann Institute, 76100, Rehovot, Israël
    • Rossignol, Raphaël. Institut de Mathématiques, Université de Neuchâtel, 11 rue Emile Argand, Case postale 158, 2009, Neuchâtel, Suisse
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Communications in Mathematical Physics, 2008, vol. 280, no. 2, p. 445-462. Springer-Verlag
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:319069
    Summary
    We study a model of random electric networks with Bernoulli resistances. In the case of the lattice $${\mathbb{Z}^2}$$ , we show that the point-to-point effective resistance between 0 and a vertex v has a variance of order at most $${({\rm log} |v|)^{\frac{2}{3}}}$$ , whereas its expected value is of order log | v|, when v goes to infinity. When d ≠ 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]