# Fluctuations of the effective conductance in a random conductor

## Applied Analysis Seminar

## Meeting Details

For more information about this meeting, contact Alexei Novikov, Mark Levi, Leonid Berlyand, Yakov Pesin.

**Speaker:** Jim Nolen, Duke University

**Abstract:** I will talk about solutions to a linear, divergence-form
elliptic PDE with conductivity coefficient that varies randomly with
respect to the spatial variable. It has been known for some time that
homogenization may occur when the coefficients are scaled suitably; this
talk is about fluctuations of the solution around its mean behavior.
Suppose an electric potential is imposed at the boundary of some
heterogeneous conducting material. Some current will flow through the
material. What is the net current? For a finite random sample of the
material, this quantity is random. In the limit of large sample size it
converges to a deterministic constant. I will describe recent results
about fluctuations of this quantity. In particular, I'll explain a
central limit theorem for the effective conductivity.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 12/09/2014

**Time:** 4:00pm - 5:00pm