Open Access
Translator Disclaimer
March 2016 Noise-stability and central limit theorems for effective resistance of random electric networks
Raphaël Rossignol
Ann. Probab. 44(2): 1053-1106 (March 2016). DOI: 10.1214/14-AOP996


We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem for the effective resistance through the discrete torus of side length $n$ in $\mathbb{Z}^{d}$, when $n$ goes to infinity.


Download Citation

Raphaël Rossignol. "Noise-stability and central limit theorems for effective resistance of random electric networks." Ann. Probab. 44 (2) 1053 - 1106, March 2016.


Received: 1 June 2012; Revised: 1 June 2014; Published: March 2016
First available in Project Euclid: 14 March 2016

zbMATH: 1347.60133
MathSciNet: MR3474467
Digital Object Identifier: 10.1214/14-AOP996

Primary: 05C21 , 60K35

Keywords: central limit theorem , conductance , Effective resistance , Efron–Stein inequality , generalized Walsh decomposition , noise sensitivity and stability , Stochastic homogenization

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 2 • March 2016
Back to Top