Events for 07/06/2017 from all calendars

Workshop in Analysis and Probability Seminar

Time: 2:00PM - 2:50PM

Location: BLOC 220

Speaker: Petros Valettas, University of Missouri

Title: Gaussian deviation inequalities for convex functions

Abstract: The concentration of measure is perhaps one of the most important tools in modern probability with various applications in asymptotic geometric analysis. In Gauss' space states that any L​-Lipschitz map f​ on ℝn​ satisfies: γn({ x: |f(x) - M|>t})≤ \exp(-t2/(2L2)), t>0,​ where M​ is a median of f​. A consequence of this inequality is that the fluctuations of f​ can be controlled by the oscillation of f​ in a dimension free manner, i.e. { Var}(f) ≤ L2​. Although both inequalities are sharp for linear functionals and more, there are many (convex) Lipschitz maps for which { Var}(f) ≪ L2​. In this talk we are going to review the reasons for which the above inequalities may fail to be tight and we shall discuss new distributional inequalities for convex maps of Gaussian vectors. We will see that for such maps a variance-sensitive, one-sided small deviation inequality can always be obtained. We will also explain how the ratio of the variance over the Lipschitz constant can quantify the tightness of the classical concentration. Based on a joint work with G. Paouris (Texas A&M).

Working Seminar on Quantum Computation and Quantum Information

Time: 2:00PM - 3:30PM

Location: BLOC 506A

Speaker: Michael Brannan, TAMU

Title: Joint entropy, mutual information, and Shannon's noisy channel coding theorem

Abstract: I will continue where Julia left off last week.