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Asymptotology
Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asym...
Interacting Stochastic Systems
The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work. This yields a reference work on results and methods that will be useful to all who work between applied probability and the physical, economic, and life sciences.
Eigenvalue Distribution of Large Random Matrices
Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach...
Surveys in Applied Mathematics
Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.
Random Matrix Methods for Machine Learning
This unified random matrix approach to large-dimensional machine learning covers applications from power detection to deep neural networks.
Frontiers in Condensed Matter Physics Research
Condensed matter is one of the most active fields of physics, with a stream of discoveries in areas from superfluidity and magnetism to the optical, electronic and mechanical properties of materials such as semiconductors, polymers and carbon nanotubes. It includes the study of well-characterised solid surfaces, interfaces and nanostructures as well as studies of molecular liquids (molten salts, ionic solutions, liquid metals and semiconductors) and soft matter systems (colloidal suspensions, polymers, surfactants, foams, liquid crystals, membranes, biomolecules etc) including glasses and biological aspects of soft matter. The book presents state-of-the-art research in this exciting field.
Multi-scale Analysis for Random Quantum Systems with Interaction
The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localizati...
Wave Propagation in Complex Media
This IMA Volume in Mathematics and its Applications WAVE PROPAGATION IN COMPLEX MEDIA is based on the proceedings of two workshops: • Wavelets, multigrid and other fast algorithms (multipole, FFT) and their use in wave propagation and • Waves in random and other complex media. Both workshops were integral parts of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Gregory Beylkin, Robert Burridge, Ingrid Daubechies, Leonid Pastur, and George Papanicolaou for their excellent work as organizers of these meetings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO, and the Office of Naval Research (ONR), whos...
Stochastic Processes, Physics and Geometry: New Interplays. I
This volume and "IStochastic Processes, Physics and Geometry: New Interplays II" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions ...
Quadrature Theory
Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which for...
