[Turkmath:7862] Seminar: Gabriel Tucci, Bell Labs : Tuesday 06, 4PM, FENS G015, SU

[Mohan Ravichandran]

Dear Colleagues,

     There will be a talk by Gabriel Tucci from Bell Labs on Sept 6,  
4PM in FENS G015 at Sabanci University. The title and the abstract are  
below

Title: Random Vandermonde Matrices and Covariance Estimates
Speaker: Gabriel Tucci, Bell Labs

Abstract:

The talk will consist of two parts. In the first part we will center  
on the limit eigenvalue distribution of random Vandermonde matrices  
with unit magnitude complex entries. The phases of the entries are  
chosen independently and identically distributed from the interval  
$[-\pi, \pi]$. Various types of distribution for the phase are  
considered and we establish the limit eigenvalue distribution in a  
wide range of cases. We also provide a combinatorial and analytic  
formula for the sequence of moments. The rate of growth of the maximum  
and minimum eigenvalue is examined.

In the second part, we will discuss a new approach to the estimation  
of covariance estimates. The estimation of a covariance matrix from  
insufficient data is one of the most common problems in multivariate  
statistics. More specifically, assume we have a set of $n$ independent  
identically distributed measurements of an $m$ dimensional random  
vector where $n<m$. The maximum likelihood estimate is the sample  
covariance matrix but in the case $n<m$ this estimate is singular, and  
therefore it is a fundamentally bad estimate. In this part we will  
discuss a new approach to this problem where we use random matrices  
techniques and free probability.

Best,
Mohan Ravichandran