OXF HANDB RANDOM MATRIX THEORY OHBK C

Erscheinungsjahr 2011
ISBN: 978-0-19-957400-1
Verlag: ACADEMIC

Buch, Englisch, 952 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 1790 g

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.

Zielgruppe

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.

Autoren/Hrsg.

Al, Akemann Et

Akemann, Gernot

Baik, Jinho

Di Francesco, Philippe

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Freeman Dyson: Forward
I Introduction
1: Gernot Akenmann, Jinho Baik & Philippe Di Francesco: Guide to the Handbook
2: Oriol Bohigas & Hans Weidenmüller: History
II Properties of Random Matrix Theory
3: Martin Zirnbauer: Symmetry Classes
4: Greg W. Anderson: Spectral Statisitics of Unitary Emsembles
5: Mark Adler: Spectral Statistics of Orthogonal and Symplectic Ensembles
6: Arno Kuijlaars: Universality
7: Thomas Guhr: Supersymmetry
8: Eugene Kanzieper: Replica Approach
9: Alexander Its: Painlevé Transcendents
10: Pierre van Moerbeke: Random Matrices and Integrable Systems
11: Alexei Borodin: Determinantal Point Processes
12: Vladimir Kravtsov: Random Matrix Representations of Critical Statistics
13: Zdzislaw Burda & Jerzy Jurkiewicz: Heavy-Tailed Random Matrices
14: Giovanni Cicuta & Luca Molinari: Phase Transitions
15: Marco Bertola: Two-Matrix Models and Biorthogonal Polynomials
16: Nicolas Orantin: Loop Equation Method
17: Alexei Morozov: Unitary Integrals and Related Matrix Models
18: Boris Khoruzhenko & Hans-Jürgen Sommers: Non-Hermitian Ensembles
19: Edouard Brézin & Sinobu Hikami: Characteristic Polynomials
20: Peter Forrester: Beta Ensembles
21: Gérard Ben Arous & Guionnet: Wigner Matrices
22: Roland Speicher: Free Probability Theory
23: Thomas Spencer: Random Banded and Sparse Matrices
III Applications of Random Matrix Theory
24: Jon Keating & Nina Snaith: Number Theory
25: Grigori Olshanski: Random Permutations
26: Jeremie Bouttier: Enumeration of Maps
27: Poul Zinn-Justin & Jean-Bernard Zuber: Knot Theory
28: Noureddine El Karoui: Multivariate Statistics
29: Leonid Chekhov: Algrebraic Geometry
30: Ian Kostov: Two-Dimensional Quantum Gravity
31: Marcos Mariño: String Theory
32: Jac Verbaarschot: Quantum Chromodynamics
33: Sebastian Müller & Martin Sieber: Quantum Chaos and Quantum Graphs
34: Yan Fyodorov & Dmitry Savin: Resonance Scattering in Chaotic Systems
35: Carlo W. J. Beenakker: Condensed Matter Physics
36: Carlo W. J. Beenakker: Optics
37: Satya N. Majumdar: Extreme Eigenvalues of Wishart Matrices and Entangled Bipartite System
38: Patrik L. Ferrari & Herbert Spohn: Random Growth Models
39: Anton Zabrodin: Laplacian Growth
40: Jean-Phillipe Bouchard & Marc Potters: Financial Applications
41: Antonia Tulino & Sergio Verdú: Information Theory
42: Graziano Vernizzi & Henri Orland: Ribonucleic Acid Folding
43: Geoff Rodgers & Taro Nagao: Complex Networks

Über Autor(innen)

Akemann, Gernot
Gernot Akemann gained his PhD in theoretical physics at Leibniz Universität Hannover in 1996. He was an EU Marie-Curie Fellow from 1996 until 1998. He has worked at MPIK Heidelberg and later at CEA SPhT, where he held a Heisenberg fellowship. He is currently Professor for Mathematical Physics at the Faculty of Physics, Bielefeld University, Germany.

Baik, Jinho
Jinho Baik gained his PhD in mathematics at New York University in 1999. He has been the recipient of the AMS Centennial Fellowship, the Sloan Research Fellowship and he won the CMFT2005 Young Researcher Award. He is currently an associate professor in the Department of Mathematics, University of Michigan.

Di Francesco, Philippe
Philippe Di Francesco gained his PhD in theoretical physics in 1989 at the Université Pierre et Marie Curie (Paris 6). He completed his habilitation in mathematics in 2004 at the Université Paris Diderot (Paris 7). He was a postdoctoral researcher in the Department of Mathematics, Princeton and a professor with the Department of Mathematics, University of North Carolina. He has been a research member of IPHT, CEA Saclay since 1989.