Speaker: Motoko Kotani, Department of Mathematics, Tohoku University, Sendai, Japan

Title: Large deviations and geometry of crystal lattices

Abstract: A crystal lattice is an abelian cover of a finite graph. Typical examples are the integer lattices, the triangular lattice and the hexagonal lattice. Large deviation holds for random walks on a crystal lattice. We will discuss how the rate function appearing in the large deviation relates with geometry of the crystal lattice. Because of the periodic structure of the crystal lattice, by reducing the scale smaller and smaller, it converges in the the Gromov-Hausdorff topology. The limit space plays an role in the large deviation theorem.

Speaker: Christian Houdré, Mathematics, Georgia Tech

Title: Concentration phenomena for ID laws: Lower and upper bounds

Abstract: I will survey some recent results giving a rather complete understanding of the concentration phenomenon for infinitely divisible laws. In the independent case, a dichotomy occurs: Under finite exponential moment conditions dimension free estimates hold true while it is not the case in general. For norms of ID vectors, complementary lower bounds will also be obtained. If time allows, applications will be presented (spectrum of random matrices with Cauchy entries, ...) This talk is mainly based on results obtained with P. Marchal and P. Reynaud.

Spring 2003
Fall 2002

ACM | CDSNS Colloquium | Colloquium | Math Seminars | Nonlinear Science | Stochastics |