This volume presents five different methods recently developed to tackle the large scale
behavior of highly correlated random systems such as spin glasses random polymers local
times and loop soups and random matrices. These methods presented in a series of lectures
delivered within the Jean-Morlet initiative (Spring 2013) play a fundamental role in the
current development of probability theory and statistical mechanics. The lectures were: Random
Polymers by E. Bolthausen Spontaneous Replica Symmetry Breaking and Interpolation Methods by
F. Guerra Derrida's Random Energy Models by N. Kistler Isomorphism Theorems by J. Rosen and
Spectral Properties of Wigner Matrices by B. Schlein. This book is the first in a co-edition
between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims
to collect together courses and lectures on cutting-edge subjects given during the term of the
Jean-Morlet Chair as well as new material produced in its wake. It is targeted at researchers
in particular PhD students and postdocs working in probability theory and statistical physics.
