TITLE

Normal approximation for a random elliptic equation

AUTHOR(S)
Nolen, James
PUB. DATE
August 2014
SOURCE
Probability Theory & Related Fields;Aug2014, Vol. 159 Issue 3/4, p661
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider solutions of an elliptic partial differential equation in $$\mathbb{R }^d$$ with a stationary, random conductivity coefficient that is also periodic with period $$L$$ . Boundary conditions on a square domain of width $$L$$ are arranged so that the solution has a macroscopic unit gradient. We then consider the average flux that results from this imposed boundary condition. It is known that in the limit $$L \rightarrow \infty $$ , this quantity converges to a deterministic constant, almost surely. Our main result is that the law of this random variable is very close to that of a normal random variable, if the domain size $$L$$ is large. We quantify this approximation by an error estimate in total variation. The error estimate relies on a second order Poincaré inequality developed recently by Chatterjee.
ACCESSION #
96985779

 

Related Articles

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics