In this book we shall analyze with techniques coming mainly from partial
differential equations (PDE) and of semi-classical analysis problems coming
from statistical mechanics.
Our main object of analysis is a (family of) measure(s) representing the
probability of presence of m particles in interaction and having the form
d/i(m) := Z(m,h)-Xex$ -^- dX
(m € IN) where
• Z(m, h) is a normalization constant,
is a C°° function defined on IRm, tending to oo at oo, with a
specific structure coming from statistical mechanics (usually a
perturbation of YL^jL i 4>(xj) taking account of the interaction between
nearest neighbours),
• h is a strictly positive parameter playing the role of an effective
planck constant,
• dX is the Lebesgue measure on Mm
• the integer m represents the cardinal of a set A in the lattice Z5
which will tend infinity.