High Dimensional Probability IX : The Ethereal Volume / / edited by Radosław Adamczak, Nathael Gozlan, Karim Lounici, Mokshay Madiman

• Autore: Adamczak Radosław
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023
• Edizione: 1st ed. 2023.
• Descrizione fisica: 1 online resource (445 pages)
• Disciplina: 519.2
• Soggetto topico: Probabilities; Statistics; Probability Theory; Probabilitats
• Soggetto genere / forma: Congressos; Llibres electrònics
• Altri autori: GozlanNathael LouniciKarim MadimanMokshay
• Nota di contenuto: Intro -- Preface -- Contents -- Part I Inequalities and Convexity -- Covariance Representations, Lp-Poincaré Inequalities, Stein's Kernels, and High-Dimensional CLTs -- 1 Introduction -- 2 Notations and Preliminaries -- 3 Representation Formulas and Lp-Poincaré 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 Santaló Inequalities -- 1 Introduction -- 2 Entropy-Transport and Inverse Santaló Inequalities -- 2.1 From Entropy-Transport to Inverse Santaló Inequalities -- 2.2 Different Equivalent Formulations of Inverse Santaló 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 Further Remarks -- 4.1 Moments -- 4.2 Upper Bounds on Upper Tails from S-Inequalities. ; 4.3 Heavy-Tailed Distributions -- 4.4 Theorem 1 in a More General Framework -- References -- Boolean Functions with Small Second-Order Influences on the Discrete Cube -- 1 Introduction -- 2 Main Results -- 3 Auxiliary Notation and Tools -- 4 Proof of the Main Results -- 5 Alternative Proof -- References -- Some Notes on Concentration for α-Subexponential Random Variables -- 1 Introduction -- 2 A Generalized Hanson-Wright Inequality -- 3 Convex Concentration for Random Variables with Bounded Orlicz Norms -- 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 -- 3.2 Self-Standardized CLTs for Method II Trimming -- 4 Appendix 1 -- 5 Appendix 2 -- References -- Functional Central Limit Theorem via Nonstationary Projective Conditions -- 1 Introduction and Notations -- 2 Projective Criteria for Nonstationary Time Series -- 2.1 Functional CLT Under the Standard Normalization n -- 2.2 A More General FCLT for Triangular Arrays -- 3 Applications -- 3.1 Application to ρ-mixing Triangular Arrays -- 3.2 Application to Functions of Linear Processes -- 3.3 Application to the Quenched FCLT -- 3.4 Application to Locally Stationary Processes -- 4 The Case of α-Dependent Triangular Arrays -- 4.1 Application to Functions of α-Dependent Markov Chains -- 4.2 Application to Linear Statistics with α-Dependent Innovations. ; 4.3 Application to Functions of a Triangular Stationary Markov Chain -- References -- Part III Stochastic Processes -- Sudakov Minoration for Products of Radial-Type Log-ConcaveMeasures -- 1 Introduction -- 2 Results -- 3 Cube-Like Sets -- 4 How to Compute Moments -- 5 Positive Process -- 6 Small Coefficients -- 7 Large Coefficients -- 8 The Partition Scheme -- References -- Lévy Measures of Infinitely Divisible Positive Processes: Examples and Distributional Identities -- 1 Introduction -- 2 Preliminaries on Lévy Measures -- 3 Illustrations -- 3.1 Poisson Process -- 3.2 Sato Processes -- 3.3 Stochastic Convolution -- 3.4 Tempered Stable Subordinator -- 3.5 Connection with Infinitely Divisible Random Measures -- 3.5.1 Cluster Representation -- 3.5.2 A Characterization of Infinitely Divisible Random Measures -- 3.5.3 A Decomposition Formula -- 3.5.4 Some Remarks -- 3.6 Infinitely Divisible Permanental Processes -- 4 Transfer of Continuity Properties -- 5 A Limit Theorem -- References -- Bounding Suprema of Canonical Processes via Convex Hull -- 1 Formulation of the Problem -- 2 Regular Growth of Moments -- 2.1 γX-Functional -- 3 Toy Case: 1-Ball -- 4 Case II. Euclidean Balls -- 4.1 Counterexample -- 4.2 4+δ Moment Condition -- 4.3 Ellipsoids -- 5 Case III. qn-Balls, 2< -- q≤∞ -- 6 Concluding Remarks and Open Questions -- References -- Part IV High-Dimensional Statistics -- Random Geometric Graph: Some Recent Developmentsand Perspectives -- 1 Introduction -- 1.1 Random Graph Models -- 1.2 Brief Historical Overview of RGGs -- 1.3 Outline -- 2 The Random Geometric Graph Model and Its Variants -- 2.1 (Soft-) Random Geometric Graphs -- 2.2 Translation Invariant Random Geometric Graphs -- 2.3 Markov Random Geometric Graphs -- 2.4 Other Model Variants -- 3 Detecting Geometry in RGGs -- 3.1 Detecting Geometry in the Dense Regime. ; 3.2 Failure to Extend the Proof Techniques to the Sparse Regime -- 3.3 Toward the Resolution of Geometry Detection -- 3.3.1 A First Improvement When d> -- n -- 3.3.2 Reaching the Polylogarithmic Regime -- 3.4 Open Problems and Perspectives -- 4 Nonparametric Inference in RGGs -- 4.1 Description of the Model and Notations -- 4.2 Estimating the Matrix of Probabilities -- 4.3 Spectrum Consistency of the Matrix of Probabilities -- 4.4 Estimation of the Envelope Function -- 4.5 Open Problems and Perspectives -- 5 Growth Model in RGGs -- 5.1 Description of the Model -- 5.2 Spectral Convergences -- 5.3 Estimation Procedure -- 5.4 Nonparametric Link Prediction -- 6 Connections with Community-Based Models -- 6.1 Extension of RGGs to Take into Account Community Structure -- 6.2 Robustness of Spectral Methods for Community Detection with Geometric Perturbations -- 6.3 Recovering Latent Positions -- 6.4 Some Perspectives -- Appendix: Outline of the Proofs of Theorems 6 and 7 -- References -- Functional Estimation in Log-Concave Location Families -- 1 Introduction -- 2 Main Results -- 3 Error Bounds for the MLE -- 4 Concentration Bounds -- 5 Bias Reduction -- 6 Minimax Lower Bounds -- References.
• Sommario/riassunto: This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.
• Titolo autorizzato: High Dimensional Probability IX
• ISBN: 3-031-26979-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910728935603321
• Lo trovi qui: Univ. Federico II
• Serie: Progress in Probability, . 2297-0428 ; ; 80