Scaling Limits Of Interacting Particle Systems

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 the appendices some tools of the 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 some standard knowledge in probability. It can be used as a support for a graduate course or a seminar in stochastic processes.