High Dimensional Probability VIII: The Oaxaca Volume

Description

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. Front Matter ....Pages i-x Jørgen Hoffmann-Jørgensen (1942–2017) (Michael B. Marcus, Goran Peskir, Jan Rosiński)....Pages 1-7 Moment Estimation Implied by the Bobkov-Ledoux Inequality (Witold Bednorz, Grzegorz Głowienko)....Pages 9-20 Polar Isoperimetry. I: The Case of the Plane (Sergey G. Bobkov, Nathael Gozlan, Cyril Roberto, Paul-Marie Samson)....Pages 21-31 Iterated Jackknives and Two-Sided Variance Inequalities (Olivier Bousquet, Christian Houdré)....Pages 33-40 A Probabilistic Characterization of Negative Definite Functions (Fuchang Gao)....Pages 41-53 Higher Order Concentration in Presence of Poincaré-Type Inequalities (Friedrich Götze, Holger Sambale)....Pages 55-69 Rearrangement and Prékopa–Leindler Type Inequalities (James Melbourne)....Pages 71-97 Generalized Semimodularity: Order Statistics (Iosif Pinelis)....Pages 99-119 Geometry of \(\ell _p^n\,\text{-Balls}\): Classical Results and Recent Developments (Joscha Prochno, Christoph Thäle, Nicola Turchi)....Pages 121-150 Remarks on Superconcentration and Gamma Calculus: Applications to Spin Glasses (Kevin Tanguy)....Pages 151-168 Asymptotic Behavior of Rényi Entropy in the Central Limit Theorem (Sergey G. Bobkov, Arnaud Marsiglietti)....Pages 169-200 Uniform-in-Bandwidth Functional Limit Laws for Multivariate Empirical Processes (Paul Deheuvels)....Pages 201-239 Universality of Limiting Spectral Distribution Under Projective Criteria (Florence Merlevède, Magda Peligrad)....Pages 241-276 Exchangeable Pairs on Wiener Chaos (Ivan Nourdin, Guangqu Zheng)....Pages 277-303 Permanental Processes with Kernels That Are Not Equivalent to a Symmetric Matrix (Michael B. Marcus, Jay Rosen)....Pages 305-320 Pointwise Properties of Martingales with Values in Banach Function Spaces (Mark Veraar, Ivan Yaroslavtsev)....Pages 321-340 Concentration Inequalities for Randomly Permuted Sums (Mélisande Albert)....Pages 341-383 Uncertainty Quantification for Matrix Compressed Sensing and Quantum Tomography Problems (Alexandra Carpentier, Jens Eisert, David Gross, Richard Nickl)....Pages 385-430 Uniform in Bandwidth Estimation of the Gradient Lines of a Density (David Mason, Bruno Pelletier)....Pages 431-455