Mathematical Methods for Hydrodynamic Limits

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.