Information Theory and Concentration Phenomena

Concentration phenomena have come to play a significant role in probability, statistics, and computer science. The purpose of this workshop is to bring together applied and theoretical researchers to stimulate further progress on concentration phenomena and its connections with other areas. Ideas from information theory and geometry can be used to establish new types of concentration inequalities, and they provide a deeper understanding of established results. In particular, geometric and entropic inequalities play an important role in finite-dimensional and asymptotic concentration phenomena. At the same time, concentration results can lead to a deeper understanding of information theory and geometry. Although these principles are well established, there have been many striking advances in recent years. Researchers have made significant progress on subadditivity of quantum information, quantitative entropy power inequalities, and concentration properties for random variables that have many symmetries (such as spin glasses and random graph models). Another line of work uses tools from quantum statistical mechanics to analyze the random matrices that arise in numerical analysis, sparse optimization, and statistics. This workshop will explore the interactions among these ideas in the hope of generating new advances.