Recueil de modèles aléatoires / Djalil Chafaï, Florent Malrieu

Bibliogr. p. 373-389. Index

This book provides a very nice collection of models in applied probability. It is organized in 27 chapters which are essentially independent of each other, and every chapter is devoted to a particular topic like tossing a coin, random walks, branching processes, records, queuing theory, reinforcement, or random matrices, to mention only a few of them.

In the discussion of each of these topics, the authors start with a brief verbal description of a general situation or problem and then pass to a model and its analysis, and in the course of the chapter the discussion proceeds to variations or extensions of the initial model and to related results. The style of the presentation is narrative and rather elegant, but the reader should be aware that many results which are mentioned in passing and may seem to be obvious do in fact need a proof.

The book is well suited as a basis for an advanced course or seminar on applied probability. To assist the selection of topics which are suitable with regard to the students’ background in probability theory, every chapter contains a list of keywords, a list of the required tools from probability theory and an indication of the degree of difficulty. On the other hand, many topics dealt with in this book could be included, e.g., in a series of lectures on Markov chains or martingales (zbMath)