This volume collects selected papers from the 8th High Dimensional Probability meeting held at Casa Matemática Oaxaca (CMO), Mexico.

High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, random graphs, information theory and convex geometry.

The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.

Jørgen Hoffmann-Jørgensen (19422017).- Moment estimation implied by the Bobkov-Ledoux inequality.- Polar Isoperimetry. I: The case of the Plane.- Iterated Jackknives and Two-Sided Variance Inequalities.- A Probabilistic Characterization of Negative Definite Functions.- Higher Order Concentration in presence of Poincaré-type inequalities.- Rearrangement and PrékopaLeindler Type Inequalities.- Generalized Semimodularity: Order Statistics.- Geometry of np -Balls: Classical Results and Recent Developments.- Remarks on Superconcentration and Gamma calculus. Application to Spin Glasses.- Asymptotic behavior of Rényi entropy in theCentral Limit Theorem.- Uniform-in-Bandwidth Functional Limit Laws for Multivariate Empirical Processes.- Universality of Limiting Spectral Distribution Under Projective Criteria.- Exchangeable Pairs on Wiener Chaos.- Permanental Processes with Kernels That Are Not Equivalent to a Symmetric Matrix.- Pointwise Properties of Martingales with Values in Banach Function Spaces.- Concentration Inequalities for Randomly Permuted Sums.- Uncertainty Quantification for Matrix Compressed Sensing and Quantum Tomography Problems.- Uniform in Bandwidth Estimation of the Gradient Lines of a Density.