Sudeep Kamath : Concentration of Measure - 2 скачать в хорошем качестве

Sudeep Kamath : Concentration of Measure - 2

Abstract: In classical probability theory, the law of large numbers and the central limit theorem provide sharp guarantees on how the average of a large number of independent and identically distributed random variables concentrates around its mean. It has however come to be discovered that ​such​ ​behavior is shared by ​many ​functions of independent random variables that don't depend too much on any one variable. Quantifying this ​concentration ​has become an important research area and has found applications in numerous fields. In this tutorial, we will explore some of the fundamental inequalities illustrating measure concentration. Specific topics include variance bounds, the entropy method, and the transportation method. We will also discuss some applications of these results. Background: A basic familiarity with probability theory will be helpful​;​ a graduate-level first course in probability theory will be more than sufficient. We will spend some time reviewing this ​​material and no pre-requisites are assumed. Recording during the thematic meeting: «Nexus of Information and Computation Theories » theJanuary 26, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent