The number π and summation by SL(2, Z)
В сборнике представлены полные тексты докладов (статьи) 2-й международной конференции по стохастическим методам и анализу данных (2nd Stochastic Modeling Techniques and Data Analysis International Conference, SMTDA-2012), которая проходила с 5 по 8 июня 2012 года в г. Ханья, Крит, Греция.
Foreword by Freeman Dyson All main theoretical aspects and current applications of random matrices are covered Complementing views of leaders in the fields of mathematics and physics Applications in all branches of physics are covered, as well as in mathematics, biology and engineering Includes most important and up to date references Provides a guide for newcomers to the field Introduces those already familiar with random matrix theory with new areas of research With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach. In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding. The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering. Readership: Suitable for mathematicians, physicists, statisticians and engineers. This handbook serves as a reference book for those already familiar with the field, as a guide to the field for newcomers and as an introduction to the wider applications of random matrix theory.