Random matrices

Friday, November 1, 2013 - 10:15am - 11:05am
Hau-tieng Wu (Stanford University)
Recently, we introduced Vector Diffusion Maps (VDM) and showed that the Connection Laplacian of the tangent bundle of the manifold can be approximated from random samples. In the first part of the talk, we will present a unified framework for approximating other Connection Laplacians over the manifold by considering its principle bundle structure. We prove that the eigenvectors and eigenvalues of these Laplacians converge in the limit of infinitely many random samples.
Tuesday, September 27, 2011 - 10:15am - 11:00am
Joel Tropp (California Institute of Technology)
We introduce a new methodology for studying the maximum eigenvalue of a sum of independent, symmetric random matrices. This approach results in a complete set of extensions to the classical tail bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Freedman, Hoeffding, and McDiarmid. Results for rectangular random matrices follow as a corollary. This research is inspired by the work of Ahlswede--Winter and Rudelson--Vershynin, but the new methods yield essential improvements over earlier results.
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