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Title The Oxford handbook of random matrix theory / editors, Gernot Akemann, Jinho Baik, Philippe Di Francesco.

Published Oxford ; New York : Oxford University Press, 2011.


Location Call No. Status
 UniM ERC  512.9434 OXFO    DUE 16-12-19
Physical description xxxi, 919 pages : illustrations ; 26 cm.
Series Oxford handbooks.
Oxford handbooks.
Bibliography Includes bibliographical references and index.
Contents Machine generated contents note: -- Forward, Freeman Dyson -- 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.
Summary "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"--
Other author Akemann, Gernot.
Baik, Jinho, 1973-
Di Francesco, Philippe.
Subject Random matrices.
Variant Title Handbook of random matrix theory.
ISBN 9780199574001 (hardback)
0199574006 (hardback)