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.
.Topical and comprehensive survey of the emerging, interdisciplinary field of "Complex Systems," covered by recognized world experts
."Les Houches lectures notes": a long tradition of excellence and long-lasting impact
.Of interest to a broad audience (mathematics, physics, biology, informatics, finance, geology, etc.)
.Some applications may have concrete impact
.Selected topics in complex systems: forefront of research in the field"

The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists.

The widespread availability of high-quality, high-frequency data has revolutionised the study of financial markets. By describing not only asset prices, but also market participants' actions and interactions, this wealth of information offers a new window into the inner workings of the financial ecosystem. In this original text, the authors discuss empirical facts of financial markets and introduce a wide range of models, from the micro-scale mechanics of individual order arrivals to the emergent, macro-scale issues of market stability. Throughout this journey, data is king. All discussions are firmly rooted in the empirical behaviour of real stocks, and all models are calibrated and evaluated using recent data from Nasdaq. By confronting theory with empirical facts, this book for practitioners, researchers and advanced students provides a fresh, new, and often surprising perspective on topics as diverse as optimal trading, price impact, the fragile nature of liquidity, and even the reasons why people trade at all.

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

This is a book about laser cooling, a new research field with many potential applications. The authors present an original approach, using the tools and concepts of statistical physics. A new understanding of laser cooling, both intuitive and quantitative, is obtained. The volume also comprises a case study allowing non-Gaussian (Lévy) statistics, a technique being used more frequently in many different fields.

This is a book about laser cooling, a new research field with many potential applications. The authors present an original approach, using the tools and concepts of statistical physics. A new understanding of laser cooling, both intuitive and quantitative, is obtained. The volume also comprises a case study allowing non-Gaussian (Lévy) statistics, a technique being used more frequently in many different fields.

Summarizing market data developments, some inspired by statistical physics, this book explains how to better predict the actual behavior of financial markets with respect to asset allocation, derivative pricing and hedging, and risk control. Risk control and derivative pricing are major concerns to financial institutions. The need for adequate statistical tools to measure and anticipate amplitude of potential moves of financial markets is clearly expressed, in particular for derivative markets. Classical theories, however, are based on assumptions leading to systematic (sometimes dramatic) underestimation of risks. First edition Hb (2000): 0-521-78232-5