Normal approximation for the net flux through a random conductor
Journal Article
© Springer Science+Business Media New York 2015. We consider solutions of an elliptic partial differential equation in Rd with a stationary, random conductivity coefficient. The boundary condition on a square domain of width L is chosen so that the solution has a macroscopic unit gradient. We then consider the average flux through the domain. It is known that in the limit L →∞, this quantity converges to a deterministic constant, almost surely. Our main result is about normal approximation for this flux when L is large: we give an estimate of the Kantorovich–Wasserstein distance between the law of this random variable and that of a normal random variable. This extends a previous result of the author (Probab Theory Relat Fields, 2013. doi:10.1007/s00440-013-0517-9) to a much larger class of random conductivity coefficients. The analysis relies on elliptic regularity, on bounds for the Green’s function, and on a normal approximation method developed by Chatterjee (Ann Probab 36:1584–1610, 2008) based on Stein’s method.
Full Text
Duke Authors
Cited Authors
- Nolen, J
Published Date
- September 1, 2016
Published In
Volume / Issue
- 4 / 3
Start / End Page
- 439 - 476
Electronic International Standard Serial Number (EISSN)
- 2194-041X
International Standard Serial Number (ISSN)
- 2194-0401
Digital Object Identifier (DOI)
- 10.1007/s40072-015-0068-4
Citation Source
- Scopus