High Dimensional Probability VII: The Cargèse Volume

Editors: Christian Houdré, David M. Mason, Patricia Reynaud-Bouret, Jan Rosiński



Gives a unique view on the mathematical methods used by experts to establish high dimensional results

Displays the wide scope of the types of problems to which these methods can be successfully applied

Provides not only a valuable introduction to what is meant by high dimensional probability, but also exposes fruitful new areas of research

This volume collects selected papers from the 7th High Dimensional Probability meeting held at the Institut d'études Scientifiques de Cargèse (IESC) in Corsica, France.

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, and random graphs.

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

Table of contents (19 chapters)

Stability of Cramer’s Characterization of Normal Laws in Information Distances

V.N. Sudakov’s Work on Expected Suprema of Gaussian Processes

Optimal Concentration of Information Content for Log-Concave Densities

Maximal Inequalities for Dependent Random Variables

On the Order of the Central Moments of the Length of the Longest Common Subsequences in Random Words

A Weighted Approximation Approach to the Study of the Empirical Wasserstein Distance

On the Product of Random Variables and Moments of Sums Under Dependence

The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach

Fechner’s Distribution and Connections to Skew Brownian Motion

Erdős-Rényi-Type Functional Limit Laws for Renewal Processes

Limit Theorems for Quantile and Depth Regions for Stochastic Processes

In Memory of Wenbo V. Li’s Contributions

Orlicz Integrability of Additive Functionals of Harris Ergodic Markov Chains

Bounds for Stochastic Processes on Product Index Spaces

Permanental Vectors and Selfdecomposability

Permanental Random Variables,

Convergence in Law Implies Convergence in Total Variation for Polynomials in Independent Gaussian, Gamma or Beta Random Variables

Perturbation of Linear Forms of Singular Vectors Under Gaussian Noise

Optimal Kernel Selection for Density Estimation