High Dimensional Probability VI, 6th Edition

  • Published By:
  • ISBN-10: 3034804903
  • ISBN-13: 9783034804905
  • DDC: 519.2
  • Grade Level Range: College Freshman - College Senior
  • 373 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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This is a collection of papers by participants at High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada. 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 areas of mathematics, statistics, and computer science. These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory. The papers in this volume show that HDP theory continues to develop new tools, methods, techniques and perspectives to analyze the random phenomena. Both researchers and advanced students will find this book of great use for learning about new avenues of research.​

Table of Contents

Front Cover.
Editorial Board.
Title Page.
Copyright Page.
1: Inequalities and Convexity.
2: Bracketing Entropy of High Dimensional Distributions.
3: Slepian's Inequality, Modularity and Integral Orderings.
4: A More General Maximal Bernstein-type Inequality.
5: Maximal Inequalities for Centered Norms of Sums of Independent Random Vectors.
6: A Probabilistic Inequality Related to Negative Definite Functions.
7: Optimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities.
8: Strong Log-concavity is Preserved by Convolution.
9: On Some Gaussian Concentration Inequality for Non-Lipschitz Functions.
10: Limit Theorems.
11: Rates of Convergence in the Strong Invariance Principle for Non-adapted Sequences. Application to Ergodic Automorphisms of the Torus.
12: On the Rate of Convergence to the Semi-circular Law.
13: Empirical Quantile CLTs for Time-dependent Data.
14: Asymptotic Properties for Linear Processes of Functional of Reversible or Normal Markov Chains.
15: Stochastic Processes.
16: First Exit of Brownian Motion from a One-sided Moving Boundary.
17: On Levy's Equivalence Theorem in Skorohod Space.
18: Continuity Conditions for a Class of Second-order Permanental Chaoses.
19: Random Matrices and Applications.
20: On the Operator Norm of Random Rectangular Toeplitz Matrices.
21: Edge Fluctuations of Eigenvalues of Wigner Matrices.
22: On the Limiting Shape of Young Diagrams Associated with Inhomogeneous Random Words.
23: High Dimensional Statistics.
24: Low Rank Estimation of Similarities on Graphs.
25: Sparse Principal Component Analysis with Missing Observations.
26: High Dimensional CLT and its Applications.