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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Normal approximation for a random elliptic PDE - N
olen\, J (Duke University)
DTSTART;TZID=Europe/London:20120914T140000
DTEND;TZID=Europe/London:20120914T145000
UID:TALK39752AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39752
DESCRIPTION:I will talk about solutions to an elliptic PDE wit
h conductivity coefficient that varies randomly wi
th respect to the spatial variable. It has been kn
own for some time that homogenization may occur wh
en the coefficients are scaled suitably. Less is k
nown about fluctuations of the solution around its
mean behaviour. For example\, imagine a conductor
with an electric potential imposed at the boundar
y. Some current will flow through the material...w
hat is the net current per unit volume? For a fini
te random sample of the material\, this quantity i
s random. In the limit of large sample size it con
verges to a deterministic constant (homogenization
). I will describe a recent result about normal ap
proximation: the probability law of the net curren
t is very close to that of a normal random variabl
e having the same mean and variance. Closeness is
quantified by an error estimate in total variation
.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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