The culmination of years of teaching experience, this book provides a modern introduction to the mathematical theory of interacting particle systems. Assuming a background in probability and measure theory, it has been designed to support a one-semester course at a Master or Ph.D. level. It also provides a useful reference for researchers, containing several results that have not appeared in print in this form before. An emphasis is placed on graphical representations, which are used to give a construction that is intuitively easier to grasp than the traditional generator approach. Also included is an extensive look at duality theory, along with discussions of mean-field methods, phase transitions and critical behaviour. The text is illustrated with the results of numerical simulations and features exercises in every chapter. The theory is demonstrated on a range of models, reflecting the modern state of the subject and highlighting the scope of possible applications.

‘This handsome volume provides an accessible introduction to one of the gems of modern probability theory. It will be valuable to those seeking a rigorous and well-illustrated account of the foundations and basic properties of Interacting Particle Systems.’

Geoffrey Grimmett - University of Cambridge

‘This book on interacting particle systems is unique, developed as a textbook for a one-semester graduate course. Technicalities are kept to a minimum, making the treatment more accessible. The reader will receive a thorough and enjoyable education about the most important models, techniques, and results.’

Rick Durrett - Duke University

‘This book serves as an important introduction to interacting particle systems, covering key foundational topics such as phase transitions, duality, and mean-field limits. The exposition is clear and well-written, with numerous examples that make the material engaging and accessible. It is particularly well-suited for Master’s and PhD students, and I will certainly recommend it to my future students and research fellows.’

Patricia Gonçalves - Instituto Superior Técnico

‘A Course in Interacting Particle Systems covers the construction, behaviour and modern tools of the most important particle systems: spin models; voter, contact and exclusion processes. It displays great intuition combined with rigorous treatment and offers an outlook to current research. Numerous exercises help the journey in a novel way — a must-have read from a top expert in the field.’

Márton Balázs - University of Bristol

‘A much-needed introduction to the field, at once accessible to beginners and informative for experienced researchers. Intuitive and inviting, it focuses on Poisson graphical constructions and features richly illustrated descriptions of model behaviour, while maintaining mathematical rigour with original formalism and clear proofs.’

Daniel Valesin - University of Warwick