书名：The Oxford Handbook of Random Matrix Theory牛津随机矩阵理论手册

作者：Gernot Akemann

出版社名称：Oxford University Press

出版时间：2015

语种：英语 

ISBN：9780198744191

商品尺寸：24.3x 17 x 5 cm

包装：平装

页数：960（以实物为准）

与Freeman Dyson的前言，手册汇集了领先的数学家和物理学家提供随机矩阵理论的全面概述，包括这一方法的新发展和应用的多样化范围的指南。

在第一部分，解决随机矩阵模型的所有现代和经典技术探索，包括正交多项式，精确复制或超对称。进一步介绍了维格纳和戴森经典高斯系综的所有主要扩展，包括稀疏、重尾、非厄米特或多矩阵模型。在第二部分，也是更大的一部分，涵盖了所有主要的应用，在学科范围从物理和数学到生物和工程。这包括标准领域，如数论，量子混沌或量子色动力学，以及最近的发展，如分区，增长模型，结理论，无线通信或生物聚合物折叠。

手册是既适合介绍新手到这一领域的研究和作为在数学，物理和工程活跃的研究人员的参考的主要来源。

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.

Gernot Akemann于1996年在汉诺威莱布尼茨大学获得理论物理学博士学位。从1996年到1998年，他是欧盟玛丽-居里研究员。他曾在MPIK Heidelberg工作，后来又在CEA SPhT工作，在那里他获得了海森堡奖学金。他目前是德国比勒费尔德大学物理系数学物理教授。

Gernot Akemann gained his PhD in theoretical physics at Leibniz Universitat 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.

I Introduction

1. Guide to the Handbook, Gernot Akenmann, Jinho Baik & Philippe Di Francesco

2. History, Oriol Bohigas & Hans Weidenmuller

II Properties of Random Matrix Theory

3. Symmetry Classes, Martin Zirnbauer

4. Spectral Statisitics of Unitary Emsembles, Greg W. Anderson

5. Spectral Statistics of Orthogonal and Symplectic Ensembles, Mark Adler

6. Universality, Arno Kuijlaars

7. Supersymmetry, Thomas Guhr

8. Replica Approach, Eugene Kanzieper

9. Painleve Transcendents, Alexander Its

10. Random Matrices and Integrable Systems, Pierre van Moerbeke

11. Determinantal Point Processes, Alexei Borodin

12. Random Matrix Representations of Critical Statistics, Vladimir Kravtsov

13. Heavy-Tailed Random Matrices, Zdzislaw Burda & Jerzy Jurkiewicz

14. Phase Transitions, Giovanni Cicuta & Luca Molinari

15. Two-Matrix Models and Biorthogonal Polynomials, Marco Bertola

16. Loop Equation Method, Nicolas Orantin

17. Unitary Integrals and Related Matrix Models, Alexei Morozov

18. Non-Hermitian Ensembles, Boris Khoruzhenko & Hans-Jurgen Sommers

19. Characteristic Polynomials, Edouard Brezin & Sinobu Hikami

20. Beta Ensembles, Peter Forrester

21. Wigner Matrices, Gerard Ben Arous & Guionnet

22. Free Probability Theory, Roland Speicher

23. Random Banded and Sparse Matrices, Thomas Spencer

III Applications of Random Matrix Theory

24. Number Theory, Jon Keating & Nina Snaith

25. Random Permutations, Grigori Olshanski

26. Enumeration of Maps, Jeremie Bouttier

27. Knot Theory, Poul Zinn-Justin & Jean-Bernard Zuber

28. Multivariate Statistics, Noureddine El Karoui

29. Algrebraic Geometry, Leonid Chekhov

30. Two-Dimensional Quantum Gravity, Ian Kostov

31. String Theory, Marcos Marino

32. Quantum Chromodynamics, Jac Verbaarschot

33. Quantum Chaos and Quantum Graphs, Sebastian Muller & Martin Sieber

34. Resonance Scattering in Chaotic Systems, Yan Fyodorov & Dmitry Savin

35. Condensed Matter Physics, Carlo W. J. Beenakker

36. Optics, Carlo W. J. Beenakker

37. Extreme Eigenvalues of Wishart Matrices and Entangled Bipartite System, Satya N. Majumdar

38. Random Growth Models, Patrik L. Ferrari & Herbert Spohn

39. Laplacian Growth, Anton Zabrodin

40. Financial Applications, Jean-Phillipe Bouchard & Marc Potters

41. Information Theory, Antonia Tulino & Sergio Verdu

42. Ribonucleic Acid Folding, Graziano Vernizzi & Henri Orland

43. Complex Networks, Geoff Rodgers & Taro Nagao