Complex Systems

Lecture Notes of the Les Houches Summer School 2006

Edited by

  • Jean-Philippe Bouchaud, Service de Physique de l'Etat Condensé, CEA-Saclay, and Science & Finance-CFM, France
  • Marc Mézard, CNRS, Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris Sud, France
  • Jean Dalibard, Ph.D., Laboratoire Kastler Brossel, ENS, Paris, France

There has been recently some interdisciplinary convergence on a number of precise topics which can be considered as prototypes of complex systems. This convergence is best appreciated at the level of the techniques needed to deal with these systems, which include: 1) A domain of research around a multiple point where statistical physics, information theory, algorithmic computer science, and more theoretical (probabilistic) computer science meet: this covers some aspects of error correcting codes, stochastic optimization algorithms, typical case complexity and phase transitions, constraint satisfaction problems. 2) The study of collective behavior of interacting agents, its impact on understanding some types of economical and financial problems, their link to population and epidemics dynamics, game theory, social, biological and computer networks and evolution.The present book is the written version of the lectures given during the Les Houches summer school session on "Complex Systems", devoted to these emerging interdisciplinary fields. The lectures consist both in a number of long methodological courses (probability theory, statistical physics of disordered systems, information theory, network structure and evolution, agent-based economics and numerical methods) and more specific, 'problem oriented' courses. Lecturers are all leading experts in their field; they have summarized recent results in a clear and authoritative manner. The "Les Houches lecture notes" have a long tradition of excellence and are often found to be useful for a number of years after they were written. The book is of interest to students and researchers with various backgrounds: probability theory, computer science, information theory, physics, finance, biology, etc.
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Book information

  • Published: August 2007
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-53006-6

Table of Contents

Chapter 1 - Monasson: Introduction to phase transitions in random optimization problemsChapter 2 - Montanari-Urbanke: Modern Coding Theory: The Statistical Mechanics and Computer Science Points of ViewChapter 3 - Parisi: Mean field theory of Spin Glasses: Statics and DynamicsChapter 4 - Majumdar: Random Matrices, The Ulam Problem, Directed Polymer and Growth Models, and Sequence MatchingChapter 5 - Kirman: Economies with Interacting AgentsChapter 6 - Sethna: Crackling Noise and Avalanches: Scaling, Critical Phenomena, and the Renormalization GroupChapter 7 - Toninelli: Bootstrap and Jamming PercolationChapter 8 - Newman: Complex NetworksChapter 9 - Challet: Minority GamesChapter 10 - Giardina: Metastable States in Glassy SystemsChapter 11 - Fisher: Evolutionary DynamicsChapter 12 - Berg: Statistical modelling and analysis of biological networksChapter 13 - Berthier: The slow dynamics of glassy materials: Insights from computer simulationsChapter 14 - Franceschelli: Epigenetic landscape and catastrophe theoryChapter 15 - Zdeborova: A Hike in the Phases of the 1-in-3 satisfiability