Noise-stability and central limit theorems for effective resistance of random electric networks

DOI10.1214/14-AOP996zbMath1347.60133arXiv1206.3856MaRDI QIDQ282503

Raphaël Rossignol

Publication date: 12 May 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3856

zbMATH Keywords

stabilitynoise sensitivitycentral limit theoremsstochastic homogenizationeffective resistanceconductanceEfron-Stein inequalitygeneralized Walsh decompositionrandom electric networks

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Special processes (60K99) Flows in graphs (05C21)

Related Items (14)

Boolean functions: influence, threshold and noise ⋮ Pointwise two-scale expansion for parabolic equations with random coefficients ⋮ Eigenvalue Fluctuations for Lattice Anderson Hamiltonians ⋮ Normal approximation for the net flux through a random conductor ⋮ High order correctors and two-scale expansions in stochastic homogenization ⋮ The structure of fluctuations in stochastic homogenization ⋮ Normal approximation for a random elliptic equation ⋮ Annealed estimates on the Green function ⋮ Effective multipoles in random media ⋮ A central limit theorem for the effective conductance: linear boundary data and small ellipticity contrasts ⋮ Scaling Limit of Fluctuations in Stochastic Homogenization ⋮ Gaussian bounds for noise correlation of resilient functions ⋮ A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus ⋮ The additive structure of elliptic homogenization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Normal approximation for a random elliptic equation
• A structure theorem for Boolean functions with small total influences
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• Exponential concentration for first passage percolation through modified Poincaré inequalities
• Submean variance bound for effective resistance of random electric networks
• Fluctuations of eigenvalues and second order Poincaré inequalities
• The diffusion limit for reversible jump processes on \(Z^ m\) with ergodic random bond conductivities
• The jackknife estimate of variance
• A lower bound on the variance of conductance in random resistor networks
• Approximation of the effective conductivity of ergodic media by periodization
• Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder
• Normal approximation under local dependence.
• A central limit theorem for the effective conductance: linear boundary data and small ellipticity contrasts
• On homogenization and scaling limit of some gradient perturbations of a massless free field
• Gaussian bounds for noise correlation of functions
• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
• Spectral homogenization of reversible random walks on \(\mathbb Z^d\) in a random environment.
• On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to \(\nabla\varphi\) interface model
• Probability on Trees and Networks
• Inégalité de Harnack elliptique sur les graphes
• On Harnack's theorem for elliptic differential equations
• Tail estimates for homogenization theorems in random media
• Noise sensitivity of Boolean functions and applications to percolation

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