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Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations
Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models. These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.
Grahame Clark and His Legacy
Grahame Clark was a major figure in European archaeology for over 50 years, and pioneered work in prehistoric economies and ecology, in science-based archaeology and in a world view of ancient societies. In this book a variety of authorities from Europe and beyond assess these major contributions and provide discussions about Clark's own colleagues and contemporaries, his major archaeological themes and his varied approaches, and his world-wide contacts and travels. The papers provide surveys and opinions on Clark's role in the development of archaeology in the 20th century, and the basis that it provided for archaeological work of today. The book will be a valuable source of evidence, ideas and references for scholars interested in the development of the discipline.
Catalogue: Authors
Its outstanding feature is the inclusion of journal articles. For more than 50 years the periodicals have been indexed, as well as compilations such as Festschriften, and the proceedings of congresses.
Asymptotic Expansion of a Partition Function Related to the Sinh-model
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.
Prehistoric Flint Mines in Europe
This volume offers a review of major flint mines dating from the Neolithic to the Bronze Age. The 18 articles were contributed by archaeologists from Belgium, France, Germany, Great Britain, Hungary, Italy, the Netherlands, Poland, Spain and Sweden, using the same framework to propose a uniform view of the mining phenomenon.
Between History and Archaeology: Papers in honour of Jacek Lech
A collection of forty-six papers papers in honour of Professor Jacek Lech, compiled in recognition of his research and academic career as well as his inquiry into the study of prehistoric flint mining, Neolithic flint tools (and beyond), and the history of archaeology.
Ludwig Faddeev Memorial Volume: A Life In Mathematical Physics
Ludwig Faddeev is widely recognized as one of the titans of 20th century mathematical physics. His fundamental contributions to scattering theory, quantum gauge theories, and the theory of classical and quantum completely integrable systems played a key role in shaping modern mathematical physics.Ludwig Faddeev's major achievements include the solution of the three-body problem in quantum mechanics, the mathematical formulation of quantum gauge theories and corresponding Feynman rules, Hamiltonian and algebraic methods in mathematical physics, with applications to gauge theories with anomalies, quantum systems with constraints and solitons, the discovery of the algebraic structure of classic...
People and the Arts in North America
"351 summaries of articles about U.S. and Canadian artists in various phases of their life and work." --Preface.
