A Course in Interacting Particle Systems

Erscheinungsjahr 2026
ISBN: 978-1-009-84347-8
Verlag: Cambridge University Press

Buch, Englisch, 182 Seiten

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

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.

Autoren/Hrsg.

Swart, Jan M.

Inhaltsverzeichnis

Preface; 1. Introduction; 2. Continuous-time Markov chains; 3. The mean-field limit; 4. Construction and ergodicity; 5. Monotonicity; 6. Duality; 7. Oriented percolation; Bibliography; Index.

Über Autor(innen)

Swart, Jan M.
Jan M. Swart is a research fellow at the Institute of Information Theory and Automation of the Czech Academy of Sciences, Prague. He has coauthored over forty papers in probability theory with an emphasis on interacting particle systems and is known, among other things, for his work on the Brownian net.