Modern Discrete Probability
An Essential Toolkit
Seiten
2024
Cambridge University Press (Verlag)
978-1-009-30511-2 (ISBN)
Cambridge University Press (Verlag)
978-1-009-30511-2 (ISBN)
This largely self-contained text introduces discrete probability and its applications, at a level suitable for beginning graduate students in mathematics, computer science, statistics and engineering. Each chapter includes exercises and pointers to the wider literature, covering a wide spectrum of essential techniques and key examples.
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.
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.
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.
Preface; Notation; 1. Introduction; 2. Moments and tails; 3. Martingales and potentials; 4. Coupling; 5. Spectral methods; 6. Branching processes; A. Useful combinatorial formulas; B. Measure-theoretic foundations; Bibliography; Index.
| Erscheinungsdatum | 09.01.2024 |
|---|---|
| Reihe/Serie | Cambridge Series in Statistical and Probabilistic Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1081 g |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| ISBN-10 | 1-009-30511-5 / 1009305115 |
| ISBN-13 | 978-1-009-30511-2 / 9781009305112 |
| Zustand | Neuware |
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