Normal approximation for a random elliptic equation

作者：Nolen James^*

来源：Probability Theory and Related Fields, 2014, 159(3-4): 661-700.

DOI：10.1007/s00440-013-0517-9

We consider solutions of an elliptic partial differential equation in with a stationary, random conductivity coefficient that is also periodic with period . Boundary conditions on a square domain of width 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 , 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 is large. We quantify this approximation by an error estimate in total variation. The error estimate relies on a second order Poincar, inequality developed recently by Chatterjee.

• 出版日期2014-8