Tel Aviv University
 
      Dear all,
       
      This week at the Horowitz seminar on Probability, Ergodic
      Theory and Dynamical Systems at Tel Aviv University we
      are happy to have Mark Rudelson from the University of
      Michigan.
      Note that Mark will also give a SECOND TALK this Sunday,
      May 13, at the Asymptotic Geometric Analysis seminar. The
      announcement for the AGA seminar is forwarded below.
 
Speaker: Mark Rudelson, University of Michigan
Title: Row products of random matrices
 
Date: Monday, May 14
Time: 14:30
Place: Schreiber 309
 
Abstract:
We study spectral and geometric properties of a certain class
of random matrices with dependent rows, which are constructed
from random matrices with independent entries. For K matrices
of size d times n we define the row product as a matrix of the
size d^K times n, whose rows are entry-wise products of the
rows of the original matrices. Such constructions arise in
several computer science problems. Simulations show that,
despite the dependency between the entries, these matrices
behave like random matrices of the same size with independent
entries. We will discuss how far this similarity can be
extended.
 
Best regards,
   Ron
Seminar webpage:
 <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html>
 
Tel Aviv University
 
**** Asymptotic Geometric Analysis seminar announcement ****
 
Dear All, 
 
I am happy to announce that on Sunday we have a
special guest speaker,  Prof. Mark Rudelson from
the University of Michigan, Ann Arbor, who will 
tell us about: The smallest singular value of a
unitary perturbed matrix See abstract below. 
 
We meet as usual at 13:10 in Schreiber 008, I hope
to see you there, 
 
Shiri.  
 
PS there will be another talk by Mark on Monday at
the probability seminar, so stay tuned. 
 
Abstract: We study the distribution of the smallest singular
value of the sum of a deterministic matrix and a random
unitary matrix, uniformly distributed with respect to the Haar
measure. A bound for this singular value arises as a condition
in the Single Ring Theorem of Guionnet, Krishnapour, and
Zeitouni. Consider a family of random matrices with given
distributions of singular values. The Single Ring Theorem
asserts that under some conditions the the empirical
distributions of eigenvalues converge do a limit density,
supported in a single ring. The conditions are of two types:
"scalar", which pertain to the original distribution of
singular values, and "matrix", which is significantly harder to
check. Our result shows that the condition of the second type
is redundant.
 
Joint work with Roman Vershynin.
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ron Peled   <peledron@gmail.com>