This book is the offspring of a summer school school Macroscopic andlarge scale phenomena:
coarse graining mean field limits and ergodicity which washeld in 2012 at the University of
Twente the Netherlands. The focus lies onmathematically rigorous methods for multiscale
problems of physical origins. Each of the four book chapters is based on a set of lectures
deliveredat the school yet all authors have expanded and refined their contributions. Francois
Golsedelivers a chapter on the dynamics of large particle systems in the mean fieldlimit and
surveys the most significant tools and methods to establish suchlimits with mathematical rigor.
Golse discusses in depth a variety of examples including Vlasov--Poisson and Vlasov--Maxwell
systems. Lucia Scardia focuseson the rigorous derivation of macroscopic models using
$Gamma$-convergence amore recent variational method which has proved very powerful for
problems inmaterial science. Scardia illustrates this by various basic examples and a
moreadvanced case study from dislocation theory. Alexander Mielke'scontribution focuses on the
multiscale modeling and rigorous analysis ofgeneralized gradient systems through the new
concept of evolutionary$Gamma$-convergence. Numerous evocative examples are given e.g.
relating toperiodic homogenization and the passage from viscous to dry friction. Martin Göll
and EvgenyVerbitskiy conclude this volume taking a dynamical systems and ergodic
theoryviewpoint. They review recent developments in the study of homoclinic pointsfor certain
discrete dynamical systems relating to particle systems viaergodic properties of lattices
configurations.
