Modern Discrete Probability: An Essential Toolkit (Cambridge Series in Statistical and Probabilistic Mathematics) - Hardcover

Roch, Sébastien

Hardcover

ISBN 10: 1009305115 ISBN 13: 9781009305112

Publisher: Cambridge University Press, 2024

Synopsis

Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering.

About this title

About the Author

Sébastien Roch is Professor of Mathematics at the University of Wisconsin, Madison. He has been awarded an NSF CAREER award, an Alfred P. Sloan Fellowship, and a Simons Fellowship in Mathematics, and is a Fellow of the Institute for Mathematical Statistics.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2024
• Language: English
• ISBN 10: 1009305115
• ISBN 13: 9781009305112
• Binding: Hardcover
• Edition number: 1
• Number of pages: 452