This volume presents five different methods recently developed to tackle the large scalebehavior of highly correlated random systems, such as spin glasses, random polymers, local times and loopsoups and random matrices.These methods, presented in a series of lectures delivered within the Jean-Morletinitiative (Spring 2013), play a fundamental role in thecurrent development of probabilitytheoryand statisticalmechanics.The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Modelsby N. Kistler, Isomorphism Theoremsby 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 Notesin 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 PhDstudents and postdocs, working in probability theory and statistical physics.
Table of Contents
1 Random Polymers.- 2 Spontaneous replica symmetry breaking and interpolation methods for complex statistical mechanics systems.- 3 Derrida’s random energy models: from spin glasses to the extremes of correlated random fields.- 4 Isomorphism Theorems: Markov processes, Gaussian processes and beyond.- 5 Spectral properties of Wigner matrices.