Entropy Inequalities, Correlation Functions, Couplings Between Stochastic Processes Are Powerful Techniques Which Have Been Extensively Used To Give Arigorous Foundation To The Theory Of Complex, Many Component Systems And To Its Many Applications In A Variety Of Fields As Physics, Biology, Population Dynamics, Economics, ... The Purpose Of The Book Is To Make Theseand Other Mathematical Methods Accessible To Readers With A Limited Background In Probability And Physics By Examining In Detail A Few Models Where The Techniques Emerge Clearly, While Extra Difficulties Arekept To A Minimum. Lanford's Method And Its Extension To The Hierarchy Of Equations For The Truncated Correlation Functions, The V-functions, Are Presented And Applied To Prove The Validity Of Macroscopic Equations Forstochastic Particle Systems Which Are Perturbations Of The Independent And Of The Symmetric Simple Exclusion Processes. Entropy Inequalities Are Discussed In The Frame Of The Guo-papanicolaou-varadhan Technique And Of Thekipnis-olla-varadhan Super Exponential Estimates, With Reference To Zero-range Models. Discrete Velocity Boltzmann Equations, Reaction Diffusion Equations And Non Linear Parabolic Equations Are Considered, As Limits Of Particles Models. Phase Separation Phenomena Are Discussed In The Context Of Glauber+kawasaki Evolutions And Reaction Diffusion Equations. Although The Emphasis Is Onthe Mathematical Aspects, The Physical Motivations Are Explained Through Theanalysis Of The Single Models, Without Attempting, However To Survey The Entire Subject Of Hydrodynamical Limits. Anna De Masi, Errico Presutti. Includes Bibliographical References. Annotation Entropy inequalities, correlation functions, couplingsbetween stochastic processes are powerful techniques whichhave been extensively used to give arigorous foundation tothe theory of complex, many component systems and to itsmany applications in a variety of fields as physics, biology, population dynamics, economics ... The purpose of the book is to make theseand othermathematical methods accessible to readers with a limitedbackground in probability and physics by examining in detaila few models where the techniques emerge clearly, whileextra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy ofequations for the truncated correlation functions, thev-functions, are presented and applied to prove the validityof macroscopic equations forstochastic particle systemswhich are perturbations of the independent and of thesymmetric simple exclusion processes. Entropy inequalitiesare discussed in the frame of the Guo-Papanicolaou-Varadhantechnique and of theKipnis-Olla-Varadhan super exponentialestimates, with reference to zero-range models. Discretevelocity Boltzmann equations, reaction diffusionequations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomenaare discussed in the context of Glauber+Kawasaki evolutionsand reaction diffusion equations. Although the emphasis isonthe mathematical aspects, the physical motivations areexplained through theanalysis of the single models, withoutattempting, however to survey the entire subject ofhydrodynamical limits Introduction....Pages 1-6 Hydrodynamic limits for independent particles....Pages 7-32 Hydrodynamics of the zero range process....Pages 33-51 Particle models for reaction-diffusion equations....Pages 52-66 Particle models for the Carleman equation....Pages 67-96 The Glauber+Kawasaki process....Pages 97-111 Hydrodynamic limits in kinetic models....Pages 112-127 Phase separation and interface dynamics....Pages 128-146 Escape from an unstable equilibrium....Pages 147-166 Estimates on the V-functions....Pages 167-188
