Claude Kipnis – författare

This book presents in a progressive way the techniques used in the proof of the hydrodynamic behavior of interacting particle systems. It starts with introductory material on independent particles and goes all the way to nongradient systems, covering the entropy and the relative entropy methods, asymmetric processes from which hyperbolic equations emerge, the equilibrium fluctuations and the large deviations theory for short-range stochastic dynamics. It reviews, in appendices, some tools of Markov process theory and derives estimates on the spectral gap of reversible, conservative generators. The book is self-contained and can be read by graduate students in mathematics or mathematical physics with standard probability background. It can be used as a support for a graduate on stochastic processes.

The idea of writing up a book on the hydrodynamic behavior of interacting particle systems was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the spring of 1988. At this time Claude wrote some notes in French that covered Chapters 1 and 4, parts of Chapters 2, 5 and Appendix 1 of this book. His intention was to prepare a text that was as self-contained as possible. lt would include, for instance, all tools from Markov process theory ( cf. Appendix 1, Chaps. 2 and 4) necessary to enable mathematicians and mathematical physicists with some knowledge of probability, at the Ievel of Chung (1974), to understand the techniques of the theory of hydrodynamic Iimits of interacting particle systems. In the fall of 1991 Claude invited me to complete his notes with him and transform them into a book that would present to a large audience the latest developments of the theory in a simple and accessible form. To concentrate on the main ideas and to avoid unnecessary technical difficulties, we decided to consider systems evolving in finite lattice spaces and for which the equilibrium states are product measures. To illustrate the techniques we chose two well-known particle systems, the generalized exclusion processes and the zero-range processes. We also conceived the book in such a manner that most chapters can be read independently of the others. Here are some comments that might help readers find their way.