Modern Discrete Probability
An Essential Toolkit

A graduate-level introduction to essential techniques and key examples in discrete probability, with applications to data science.

Sébastien Roch (Author)

9781009305112, Cambridge University Press

Hardback, published 18 January 2024

452 pages
26 x 18 x 2.7 cm, 1.099 kg

'Modern Discrete Probability is essential reading for any graduate student in probability and fills an important gap in the graduate probability curricula. By focusing on the core underlying techniques, it gives a picture of their broad applicability across the field. At the same time readers will learn about percolation, random walks, random graphs and spin systems that make up the building blocks of so much of probability theory.' Allan Sly, Princeton University

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.

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.

Subject Areas: Probability & statistics [PBT]