Normal approximation for the net flux through a random conductor

DOI10.1007/s40072-015-0068-4zbMath1353.35042arXiv1406.2186OpenAlexW2263345107MaRDI QIDQ338200

Mohammad Hasan, M. Dambrine

Publication date: 4 November 2016

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.2186

zbMATH Keywords

random mediastochastic homogenizationKantorovich-Wasserstein distancerandom conductance

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random operators and equations (aspects of stochastic analysis) (60H25) Second-order elliptic equations (35J15) PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (6)

High order correctors and two-scale expansions in stochastic homogenization ⋮ The structure of fluctuations in stochastic homogenization ⋮ Scaling Limit of Fluctuations in Stochastic Homogenization ⋮ A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus ⋮ The choice of representative volumes in the approximation of effective properties of random materials ⋮ The additive structure of elliptic homogenization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Noise-stability and central limit theorems for effective resistance of random electric networks
• Annealed estimates on the Green functions and uncertainty quantification
• Normal approximation for a random elliptic equation
• Recent progress on the random conductance model
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• A sharp bound on the \(L^2\) norm of the solution of a random elliptic difference equation
• Annealed estimates on the Green function
• A new method of normal approximation
• Fluctuations of eigenvalues and second order Poincaré inequalities
• An Efron-Stein inequality for nonsymmetric statistics
• The jackknife estimate of variance
• The Green function for uniformly elliptic equations
• A lower bound on the variance of conductance in random resistor networks
• Approximation of the effective conductivity of ergodic media by periodization
• Approximations of effective coefficients in stochastic homogenization
• Green's functions for elliptic and parabolic equations with random coefficients
• Elliptic partial differential equations of second order
• Quantitative results on the corrector equation in stochastic homogenization
• Averaging of symmetric diffusion in random medium
• A central limit theorem for the effective conductance: linear boundary data and small ellipticity contrasts
• Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
• On homogenization and scaling limit of some gradient perturbations of a massless free field
• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to \(\nabla\varphi\) interface model
• Random integrals and correctors in homogenization
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Fluctuation of Solutions to Linear Elliptic Equations with Noisy Diffusion Coefficients
• Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
• Tail estimates for homogenization theorems in random media
• Random heterogeneous materials. Microstructure and macroscopic properties

This page was built for publication: Normal approximation for the net flux through a random conductor