Title: Introduction to concentration inequalities, I
Speaker: Mark Meckes (Associate Professor, Department of Mathematics, Applied Mathematics, & Statistics, Case Western Reserve University)
Abstract: Measure concentration is an extremely useful phenomenon that appears in a wide variety of high-dimensional settings, and has become an indispensable tool in many areas of probability, geometry, and theoretical computer science. Roughly, it states that in many settings, a smooth function of many variables is almost equal to a constant on most of its domain. In these talks I will survey some of the most useful settings in which measure concentration occurs, present applications in various fields, and finally survey some of the most important techniques for proving concentration inequalities.
In the first talk, I will begin with concentration inequalities for sums of independent random variables.