Sep 12, 2006 4:00pm, Room 5417 Edit Delete B/W(color)Hard CopyEmail Entry
Speaker	Jay Rosen , City University of New York
Title	Frequent Points and Harnack Inequalities for Random Walks in Two Dimensions
Abstract	For a random walk in \Z2 which does not necessarily have bounded range we study those points which are visited an unusually large number of times. We prove the analogue of the Erdös-Taylor conjecture and obtain the asymptotics for the number of visits to the most visited site. We also obtain the asymptotics for the number of points which are visited very frequently by time n. The key to these results are good Harnack Inequalities for the interior and exterior of a disc. Joint work with Rich Bass.
Oct 17, 2006 4:00pm, Room 5417 Edit Delete B/W(color)Hard CopyEmail Entry
Speaker	Michael Marcus, CUNY
Title	Central limit theorems for moduli of continuity of Gaussian processes
Oct 24, 2006 4:00pm, Room 5417 Edit Delete B/W(color)Hard CopyEmail Entry
Speaker	Van Vu, Rutgers
Title	Central limit theorems for random polytopes.
Abstract	Let K be a convex body in Rd, (where d is fixed, say 4) with unit volume. Sample n points in K, randomly and independently with respect to the uniform distribution. The convex hull of these points (called Kn) is a classicial model for random polytopes. The study of random polytopes was started systematically by Renyi and Sulanke in the 1960s. One of the major questions in this field is to prove central limit theorems (as n tends to infinity) for the key parameters (such as volume or number of vertices) of Kn. I will survey recent developments that lead to the solution of this problem.
Dec 12, 2006 4:00pm, Room 5417 Edit Delete B/W(color)Hard CopyEmail Entry
Speaker	Richard Gundy, Rutgers Univ
Title	Ergodic theory of low-pass filters
Abstract	I will talk about a problem that originated in the theory of wavelets: the characterization of functions that generate multi- resolution analyses. The initial results, with Dobric and Hitczenko, were significant but the proofs were complicated. With the benefit of hindsight, the ideas can be made very simple. It turns out that we are led to the study of a basic "historical Markov process" of the type encountered in statistical mechanics, and the set of invariant measures associated with this process. The wavelet setting presents some new features of these processes. If time permits, I will show how to obtain the basic class of lowpass polynomial filters, first discovered by Ingrid Daubechies in 1986 from elementary probability considerations, going back to 1634,( the correspondence between Pascal and Fermat.)