This volume, *High Dimensional Probability VI: The Banff Volume*, is a collection of papers presented at the Sixth International Conference on High Dimensional Probability (HDP VI) held at the Banff International Research Station in Canada in October 2011. The conference brought together mathematicians and researchers interested in high-dimensional probability, a field that has seen significant growth and expansion since its inception with the *International Conferences in Probability in Banach Spaces* starting in 1975. The book is organized into five main sections: Inequalities and Convexity, Limit Theorems, Stochastic Processes, Random Matrices, and High Dimensional Statistics. Each section includes a variety of contributions that showcase the breadth and depth of high-dimensional probability. Key topics include: - **Inequalities and Convexity**: Papers cover bounds on bracketing entropies, extensions of Slepian’s inequality, maximal Bernstein-type inequalities, and concentration inequalities. - **Limit Theorems**: Contributions explore rates of convergence in strong invariance principles, empirical quantile central limit theorems, and asymptotic properties of linear processes. - **Stochastic Processes**: Research focuses on the first exit of Brownian motion from moving boundaries, Lévy’s equivalence theorem in Skorohod space, and continuity conditions for permanental chaoses. - **Random Matrices and Applications**: Papers discuss operator norms of random Toeplitz matrices, edge fluctuations of eigenvalues in Wigner matrices, and the limiting shape of Young diagrams. - **High Dimensional Statistics**: Contributions address low-rank estimation on graphs, sparse principal component analysis with missing data, and high-dimensional central limit theorems. The book is dedicated to the memory of Wenbo Li, a prominent figure in the field who passed away recently. His contributions and presence will be deeply missed by the community.This volume, *High Dimensional Probability VI: The Banff Volume*, is a collection of papers presented at the Sixth International Conference on High Dimensional Probability (HDP VI) held at the Banff International Research Station in Canada in October 2011. The conference brought together mathematicians and researchers interested in high-dimensional probability, a field that has seen significant growth and expansion since its inception with the *International Conferences in Probability in Banach Spaces* starting in 1975. The book is organized into five main sections: Inequalities and Convexity, Limit Theorems, Stochastic Processes, Random Matrices, and High Dimensional Statistics. Each section includes a variety of contributions that showcase the breadth and depth of high-dimensional probability. Key topics include: - **Inequalities and Convexity**: Papers cover bounds on bracketing entropies, extensions of Slepian’s inequality, maximal Bernstein-type inequalities, and concentration inequalities. - **Limit Theorems**: Contributions explore rates of convergence in strong invariance principles, empirical quantile central limit theorems, and asymptotic properties of linear processes. - **Stochastic Processes**: Research focuses on the first exit of Brownian motion from moving boundaries, Lévy’s equivalence theorem in Skorohod space, and continuity conditions for permanental chaoses. - **Random Matrices and Applications**: Papers discuss operator norms of random Toeplitz matrices, edge fluctuations of eigenvalues in Wigner matrices, and the limiting shape of Young diagrams. - **High Dimensional Statistics**: Contributions address low-rank estimation on graphs, sparse principal component analysis with missing data, and high-dimensional central limit theorems. The book is dedicated to the memory of Wenbo Li, a prominent figure in the field who passed away recently. His contributions and presence will be deeply missed by the community.