High dimensional probability IX : the ethereal volume / Radoslaw Adamczak, Nathael Gozlan, Karim Lounici, Mokshay Madiman, editors.

Intro
Preface
Contents
Part I Inequalities and Convexity
Covariance Representations, Lp-Poincar ̌Inequalities, Stein's Kernels, and High-Dimensional CLTs
1 Introduction
2 Notations and Preliminaries
3 Representation Formulas and Lp-Poincar ̌Inequalities
4 Stein's Kernels and High-Dimensional CLTs
5 Appendix
References
Volume Properties of High-Dimensional Orlicz Balls
1 Notation and Statement
2 Probabilistic Formulation
3 Probabilistic Preliminaries
4 Proof of Theorem 2.1
5 Application to Spectral Gaps
6 Asymptotic Independence of Coordinates

7 Integrability of Linear Functionals
References
Entropic Isoperimetric Inequalities
1 Introduction
2 Nagy's Theorem
3 One Dimensional Isoperimetric Inequalities for Entropies
4 Special Orders
5 Fisher Information in Higher Dimensions
6 Two Dimensional Isoperimetric Inequalities for Entropies
7 Isoperimetric Inequalities for Entropies in Dimension n=3 and Higher
References
Transport Proofs of Some Functional Inverse Santal ̤Inequalities
1 Introduction
2 Entropy-Transport and Inverse Santal ̤Inequalities

2.1 From Entropy-Transport to Inverse Santal ̤Inequalities
2.2 Different Equivalent Formulations of Inverse Santal ̤Inequalities
3 Proofs of Entropy-Transport Inequalities in Dimension 1
3.1 The One-Dimensional Symmetric Case
3.2 The One-Dimensional General Case
4 Revisiting the Unconditional Case
Appendix: Proof of Lemma 2.2
References
Tail Bounds for Sums of Independent Two-Sided Exponential Random Variables
1 Introduction
2 Proof of Theorem 1
3 Generalisations
3.1 Examples
3.2 Proof of Theorem 4: The Upper Bound
3.3 Proof of Theorem 4: The Lower Bound

4 Uniform Tail Bounds for First- and Second-Order Chaos
5 Random Tensors
Appendix A
References
Part II Limit Theorems
Limit Theorems for Random Sums of Random Summands
1 Introduction and Statement of Results
2 Concentration and Convergence
2.1 General Concentration
2.2 Convergence Conditions
3 Proofs of Main Results
References
A Note on Central Limit Theorems for Trimmed Subordinated Subordinators
1 Introduction
2 Two Methods of Trimming W
3 Self-Standardized CLTs for W
3.1 Self-Standardized CLTs for Method I Trimming