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Integrable Systems and Random Matrices
This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.
Spectral Theory and Differential Equations
This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in that broad spectrum of areas.
An Introduction to Random Matrices
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Mathematical Results in Quantum Mechanics
This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schrödinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires.
Algebraic and Geometric Methods in Mathematical Physics
Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Spectral Operator Theory and Related Topics
"The collection contains the papers of mathematicians who are participants of the seminar on Mathematical Physics in Kharkov, Ukraine. The papers are mainly devoted to nontraditional problems of spectral theory, of disordered systems, to the spectral aspects of homogenization, and of properties of ergodic dynamical systems."--ABSTRACT.
Topics in Random Matrix Theory
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Xviith International Congress On Mathematical Physics
The International Congress on Mathematical Physics is a major conference in its field that attracts a very wide spectrum of researchers. Held every three years, it provides an overview of recent developments and achievements in mathematical physics. This volume presents the plenary lectures and invited topical session lectures from the XVIIth ICMP, which was held in Aalborg, Denmark, August 2012. It also includes additional material from the Congress.In this volume, one can find survey lectures on orthogonal polynomials, random systems, information theory in physics, several aspects of quantum field theory and quantum mechanics, general relativity, and classical and quantum dynamical systems.The topical sessions covered the following areas:Readers are exposed to state-of-the-art views on mathematical physics. Several of the plenary lectures give broad surveys on recent activities, for example, in orthogonal polynomials, PDE in mathematical physics, and information theory in physics.
Logarithmic Potentials with External Fields
In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical...
