TY - GEN AU - Gayrard,Veronique AU - Kistler,Nicola TI - Correlated random systems : five different methods : : CIRM Jean-Morlet Chair, Spring 2013 T2 - Lecture notes in mathematics ; SN - 9783319176734 U1 - 519.23 23 PY - 2015/// CY - Switzerland PB - Springer KW - Random fields. KW - Probabilities. N1 - Random Polymers -- Spontaneous replica symmetry breaking and interpolation methods for complex statistical mechanics systems -- Derrida's random energy models: from spin glasses to the extremes of correlated random fields -- Isomorphism Theorems: Markov processes, Gaussian processes and beyond -- Spectral properties of Wigner matrices N2 - 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. ER -