Fluctuations of the effective conductance in a random conductor
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
Time: 4:00pm - 5:00pm