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>