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Case Western Reserve University DEPARTMENT OF MATHEMATICS |
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DEPARTMENT OF MATHEMATICS SEMINARS and COLLOQUIUMANALYSIS |
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Professor Pawel WOLFF Case Western Reserve University Department of Mathematics "Gaussian concentration and random multilinear forms II" Date:Tuesday, November 3, 2009 Time: 2:45-4:00 p.m. Location: Department of Mathematics, Yost 321B
ABSTRACT In the first part of the talk I will recall an elementary proof of Gaussian concentration due to Maurey and Pisier. As one of application, a sharp deviation inequality for Gaussian random bilinear forms will be shown. In the second part, the technique of Maurey-Pisier will be used to establish some new version of Gaussian concentration inequality. I will also comment on possible applications.
Professor Pawel WOLFF Case Western Reserve University Department of Mathematics "Gaussian concentration and random multilinear forms III" Date: Tuesday, November 10, 2009 Time: 2:45-4:00 p.m. Location: Department of Mathematics, Yost 321B
ABSTRACT In the first part of the talk I will recall an elementary proof of Gaussian concentration due to Maurey and Pisier. As one of application, a sharp deviation inequality for Gaussian random bilinear forms will be shown. In the second part, the technique of Maurey-Pisier will be used to establish some new version of Gaussian concentration inequality. I will also comment on possible applications.
Professor Elizabeth MECKES Case Western Reserve University Department of Mathematics "Approximation of random measures" Date: Tuesday, November 17, 2009 Time: 2:45-4:00 p.m. Location: Department of Mathematics, Yost 321B
ABSTRACT There is a large class of results which say that, for parametrized collection of random variables, a random variable from the collection behaves a certain way for “most” values of the parameter. A nice example of such a result is a theorem of Persi Diaconis and David Freedman, which roughly says that if you have a large collection of high-dimensional data points, most one- dimensional projections of the data will look Gaussian even if the data have no particular structure. Another example is the central limit property of convex bodies, namely, that most fixed-dimensional projections of uniform measure on a high-dimensional convex body are close to Gaussian. In this series of talks, I'll discuss an approach to this type of result which obtains quantitative information about fixed high dimensions. The approach uses Stein's method, the concentration of measure phenomenon, and the entropy of certain function spaces.
Professor Alexander FISH University of Wisconsin, Madison Department of Mathematics "Additive combinatorics in integers - a dynamical approach" Date: Tuesday, November 24, 2009 Time: 2:45-4:00 p.m. Location: Department of Mathematics, Yost 321B
ABSTRACT We will talk about an additional structure that we can find in A+B for A,B subsets of integers having positive upper Banach density. The classical theorem of Folner which answers the question in the special case B = -A will be reviewed. A recent combinatorial result of Jin will be reproved by use of Furstenberg's correspondence principle (methods of Ergodic Theory). If time will permit, we will motivate and formulate an inverse sumsets conjecture.
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