Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by accretion. This book, by the author of the acclaimed Lévy Processes, is the first comprehensive theoretical account of mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. This self-contained treatment develops the models in a way that makes recent developments in the field accessible. Each chapter ends with a comments section in which important aspects not discussed in the main part of the text (often because the discussion would have been too technical and/or lengthy) are addressed and precise references are given. Written for readers with a solid background in probability, its careful exposition allows graduate students, as well as working mathematicians, to approach the material with confidence.

• Author is the world-leading expert on the field and a great expositor • The first book on an important class of stochastic models • Wide-ranging areas of application - computer science, physics, geophysics, biology and more

### Contents

Introduction; 1. Self-similar fragmentation chains; 2. Random partitions; 3. Exchangeable fragmentations; 4. Exchangeable coalescents; 5. Asymptotic regimes in stochastic coalescence; References; List of symbols; Index.

### Reviews

'… an authoritative and important contribution to the research literature.' Zentralblatt MATH

' … this gem of a monograph, written with a quintessentially French style and clarity, provides a self-contained account of a recently emerged topic that will be seen as a cornerstone for future theoretical developments … it succeeds wonderfully as an authoritative account of the setup and the key results on fragmentation and coalescence' SIAM

'… clearly and concisely written … I recommend the book to any probabilist interested in theory and applications of fragmentation and coagulation processes, as well as in a clear explanation of the methodology used therein … for a PhD-course on the topic, it is a great source.' Niew Archief voor Wiskande