Random matrix theory is applied by physicists and mathematicians to understand phenomena in nature and deep mathematical structures. This book offers a comprehensive look at random matrix theory by leading researchers, including applications inside and outside of physics and mathematics.
| |
| |
| Forward | |
| |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Guide to the Handbook | |
| |
| |
| |
| |
| History | |
| |
| |
| |
| |
| Properties of Random Matrix Theory | |
| |
| |
| |
| Symmetry Classes | |
| |
| |
| |
| |
| Spectral Statisitics of Unitary Emsembles | |
| |
| |
| |
| |
| Spectral Statistics of Orthogonal and Symplectic Ensembles | |
| |
| |
| |
| |
| Universality | |
| |
| |
| |
| |
| Supersymmetry | |
| |
| |
| |
| |
| Replica Approach | |
| |
| |
| |
| |
| Painleve Transcendents | |
| |
| |
| |
| |
| Random Matrices and Integrable Systems | |
| |
| |
| |
| |
| Determinantal Point Processes | |
| |
| |
| |
| |
| Random Matrix Representations of Critical Statistics | |
| |
| |
| |
| |
| Heavy-Tailed Random Matrices | |
| |
| |
| |
| |
| Phase Transitions | |
| |
| |
| |
| |
| Two-Matrix Models and Biorthogonal Polynomials | |
| |
| |
| |
| |
| Loop Equation Method | |
| |
| |
| |
| |
| Unitary Integrals and Related Matrix Models | |
| |
| |
| |
| |
| Non-Hermitian Ensembles | |
| |
| |
| |
| |
| Characteristic Polynomials | |
| |
| |
| |
| |
| Beta Ensembles | |
| |
| |
| |
| |
| Wigner Matrices | |
| |
| |
| |
| |
| Free Probability Theory | |
| |
| |
| |
| |
| Random Banded and Sparse Matrices | |
| |
| |
| |
| |
| Applications of Random Matrix Theory | |
| |
| |
| |
| Number Theory | |
| |
| |
| |
| |
| Random Permutations | |
| |
| |
| |
| |
| Enumeration of Maps | |
| |
| |
| |
| |
| Knot Theory | |
| |
| |
| |
| |
| Multivariate Statistics | |
| |
| |
| |
| |
| Algrebraic Geometry | |
| |
| |
| |
| |
| Two-Dimensional Quantum Gravity | |
| |
| |
| |
| |
| String Theory | |
| |
| |
| |
| |
| Quantum Chromodynamics | |
| |
| |
| |
| |
| Quantum Chaos and Quantum Graphs | |
| |
| |
| |
| |
| Resonance Scattering in Chaotic Systems | |
| |
| |
| |
| |
| Condensed Matter Physics | |
| |
| |
| |
| |
| Optics | |
| |
| |
| |
| |
| Extreme Eigenvalues of Wishart Matrices and Entangled Bipartite System | |
| |
| |
| |
| |
| Random Growth Models | |
| |
| |
| |
| |
| Laplacian Growth | |
| |
| |
| |
| |
| Financial Applications | |
| |
| |
| |
| |
| Information Theory | |
| |
| |
| |
| |
| Ribonucleic Acid Folding | |
| |
| |
| |
| |
| Complex Networks | |
| |
