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.
| ISBN | 0199574006 | | Pages | 952 | | ISBN13 | 9780199574001
(What's this?) | | Weight (grammes) | 1782 | | Publisher | Oxford University Press | | Published in | Oxford | | Imprint | Oxford University Press | | Series title | Oxford Handbooks in Mathematics | | Format | Hardback | | Height (mm) | 253 | | Publication date | 28 Jul 2011 | | Width (mm) | 181 | | DEWEY | 512.5 | | Spine width (mm) | 58 | | DEWEY edition | DC23 | | Academic level | Postgraduate |
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Forward; I INTRODUCTION; 1. Guide to the Handbook; 2. History; II PROPERTIES OF RANDOM MATRIX THEORY; 3. Symmetry Classes; 4. Spectral Statisitics of Unitary Emsembles; 5. Spectral Statistics of Orthogonal and Symplectic Ensembles; 6. Universality; 7. Supersymmetry; 8. Replica Approach; 9. Painleve Transcendents; 10. Random Matrices and Integrable Systems; 11. Determinantal Point Processes; 12. Random Matrix Representations of Critical Statistics; 13. Heavy-Tailed Random Matrices; 14. Phase Transitions; 15. Two-Matrix Models and Biorthogonal Polynomials; 16. Loop Equation Method; 17. Unitary Integrals and Related Matrix Models; 18. Non-Hermitian Ensembles; 19. Characteristic Polynomials; 20. Beta Ensembles; 21. Wigner Matrices; 22. Free Probability Theory; 23. Random Banded and Sparse Matrices; III APPLICATIONS OF RANDOM MATRIX THEORY; 24. Number Theory; 25. Random Permutations; 26. Enumeration of Maps; 27. Knot Theory; 28. Multivariate Statistics; 29. Algrebraic Geometry; 30. Two-Dimensional Quantum Gravity; 31. String Theory; 32. Quantum Chromodynamics; 33. Quantum Chaos and Quantum Graphs; 34. Resonance Scattering in Chaotic Systems; 35. Condensed Matter Physics; 36. Optics; 37. Extreme Eigenvalues of Wishart Matrices and Entangled Bipartite System; 38. Random Growth Models; 39. Laplacian Growth; 40. Financial Applications; 41. Information Theory; 42. Ribonucleic Acid Folding; 43. Complex Networks
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