## Seminar:

Fall 2008, Thursdays, Milner 216, 4:00-4:50 PM

Date: October 2

"  Haar Integration and Dimensionality Reduction for Covariance Estimates "
Gabriel Tucci

Abstract

In many situations, given a sequence of $n$ random variables the covariance matrix is not know but has to be estimated. In the case we have $m$ observations and $m>>n$ then the sample covariance matrix is a good approximation of the true covariance. More specifically, for a fixed number of variables the sample covariance matrix converges with $m$ to the true covariance. However, in applications like weather forecast, wireless communications (MIMO channels with a big number of antennas), linear estimation and military applications the number of observations is limited and usually one has $m\leq n$. In this talk we will discuss what can be done in this scenario. This is based on a project done at Bell Labs with Tom Marzetta and Steve Simon where we used techniques from random matrices, free probability and representation theory.

The talk will be self-contained and we will review all technical background necessary.