High-Dimensional Probability

Roman Vershynin is Professor of Mathematics at the University of California, Irvine. He is an expert on randomness in mathematics and data science, especially in high-dimensional probability, statistics, and machine learning. His influential work has earned numerous honors including an invited ICM lecture, the Bessel Research Award, the IMS Medallion Award, and the 2019 PROSE Award for the first edition of this book.

'This book is a must-read for anyone interested in high-dimensional probability or its applications to data science. The second edition retains the enlightened selection of topics of the first edition, but with a more streamlined and self-contained exposition. The addition of an introductory chapter that serves as a refresher of basic concepts, and a wealth of new exercises at different levels should make the book appealing to an even broader audience.' Kavita Ramanan, Brown University

• Foreword Sara van de Geer; Preface; Appetizer. Using probability to cover a set; 1. A quick refresher on analysis and probability; 2. Concentration of sums of independent random variables; 3. Random vectors in high dimensions; 4. Random matrices; 5. Concentration without independence; 6. Quadratic forms, symmetrization, and contraction; 7. Random processes; 8. Chaining; 9. Deviations of random matrices on sets; Hints for the exercises; References; Index.