This volume is the result of the Sixth High Dimensional Probability Conference (HDP VI), held at the Banff International Research Station in Canada in October 2011. It contains contributions from researchers in high dimensional probability, covering a wide range of topics including inequalities and convexity, limit theorems, stochastic processes, random matrices, and high dimensional statistics. The papers illustrate the breadth and depth of high dimensional probability, showing its continued growth and importance in mathematical research. The conference was organized by Christian Houdré, David M. Mason, Jan Rosiński, and Jon A. Wellner. The participants include leading researchers in probability and statistics from around the world. The volume includes 25 papers, each presenting original research in various aspects of high dimensional probability. The first part of the volume focuses on inequalities and convexity, including topics such as bracketing entropy, Slepian's inequality, and concentration inequalities. The second part covers limit theorems, including convergence rates for non-adapted sequences and the semi-circular law. The third part discusses stochastic processes, including Brownian motion and Lévy's equivalence theorem. The fourth part deals with random matrices and their applications, while the fifth part focuses on high dimensional statistics, including principal component analysis and estimation of similarities on graphs. The papers in this volume demonstrate the continued vitality and expansion of high dimensional probability as a field of mathematical research. They use a variety of techniques in their analysis that should be of interest to advanced students and researchers. The contributions highlight the importance of high dimensional probability in various areas of mathematics and statistics, including convex geometry, asymptotic geometric analysis, additive combinatorics, and random matrices. The volume is a valuable resource for researchers and students interested in high dimensional probability and related fields.This volume is the result of the Sixth High Dimensional Probability Conference (HDP VI), held at the Banff International Research Station in Canada in October 2011. It contains contributions from researchers in high dimensional probability, covering a wide range of topics including inequalities and convexity, limit theorems, stochastic processes, random matrices, and high dimensional statistics. The papers illustrate the breadth and depth of high dimensional probability, showing its continued growth and importance in mathematical research. The conference was organized by Christian Houdré, David M. Mason, Jan Rosiński, and Jon A. Wellner. The participants include leading researchers in probability and statistics from around the world. The volume includes 25 papers, each presenting original research in various aspects of high dimensional probability. The first part of the volume focuses on inequalities and convexity, including topics such as bracketing entropy, Slepian's inequality, and concentration inequalities. The second part covers limit theorems, including convergence rates for non-adapted sequences and the semi-circular law. The third part discusses stochastic processes, including Brownian motion and Lévy's equivalence theorem. The fourth part deals with random matrices and their applications, while the fifth part focuses on high dimensional statistics, including principal component analysis and estimation of similarities on graphs. The papers in this volume demonstrate the continued vitality and expansion of high dimensional probability as a field of mathematical research. They use a variety of techniques in their analysis that should be of interest to advanced students and researchers. The contributions highlight the importance of high dimensional probability in various areas of mathematics and statistics, including convex geometry, asymptotic geometric analysis, additive combinatorics, and random matrices. The volume is a valuable resource for researchers and students interested in high dimensional probability and related fields.