| Preface.- Random Matrices and Number Theory |
| Introduction / 1： |
| Characteristic polynomials of random unitary matrices / 3： |
| Other compact groups / 4： |
| Families of L-functions and Symmetry / 5： |
| Asymptotic expansions. References / J.P. Keating6： |
| 2D Quantum Gravity, Matrix Models and Graph Combinatorics |
| Matrix models for 2D quantum gravity / 2： |
| The one-matrix model I: large N limit and the enumeration of planar graphs |
| The trees behind the graphs |
| The one-matrix model II: topological expansions and quantum gravity |
| The combinatorics beyond matrix models: geodesic distance in planar graphs |
| Planar graphs as spatial branching processes / 7： |
| Conclusion / P. Di Francesco8： |
| Eigenvalue Dynamics, Follytons and Large N Limits of Matrices |
| References / J. Arnlind ; J. Hoppe |
| Random Matrices and Supersymmetry in Disordered Systems. Supersymmetry method |
| Wave functions fluctuations in a finite volume |
| Multifractality |
| Recent and possible future developments |
| Summary |
| Acknowledgements |
| Hydrodynamics of Correlated Systems / K.B. Efetov |
| Instanton or rare fluctuation method |
| Hydrodynamic approach |
| Linearized hydrodynamics or bosonization |
| EFP through an asymptotics of the solution |
| Free fermions |
| Calogero-Sutherland model |
| Free fermions on the lattice |
| Appendix: Hydrodynamic approach to non-Galilean invariant systems / 9： |
| Appendix: Exact results for EFP in some integrable models |
| QCD, Chiral Random Matrix Theory and Integrability / A.G. Abanov |
| QCD |
| The Dirac Spectrum in QCD |
| Low Energy Limit of QCD |
| Chiral RMT and the QCD Dirac Spectrum |
| Integrability and the QCD Partition Function |
| QCD at Finite Baryon Density |
| Full QCD at Nonzero Chemical Potential |
| Conclusions / 10： |
| Euclidan Random Matrices: Solved and Open Problems / J.J. M. Verbaarschot |
| Basic definitions |
| Physical motivations |
| Field theory |
| The simplest case |
| Phonnos. References / G. Parisi |
| Matrix Models and Growth Processes |
| Some ensembles of random matrices with complex eigenvalues |
| Exact results at finite N |
| Large N limit |
| The matrix model as a growth problem. References / A. Zabrodin |
| Matrix Models and Topological Strings |
| Matrix models |
| Type B topological strings and matrix models |
| Type A topological strings, Chern-Simons theory and matrix models / M. Marino |
| Matrix Models of Moduli Space |
| Moduli Space of Riemann Surfaces and its Topology |
| Quadratic Differentials and Fatgraphs |
| The Penner model |
| Penner Model and Matrix Gamma Function |
| The Kontsevich Model |
| Applications to String Theory |
| Conclusions. References / S. Mukhi |
| Matrix Models and 2D String Theory |
| An overview of string theory |
| Strings in D-dimensional spacetime |
| Discretized surfaces and 2D string theory |
| An overview of observables |
| Sample calculation: the disk one-point function |
| Worldsheet description of matrix eigenvalues |
| Further results |
| Open problems |
| Matrix Models as Conformal Field Theories / E.J. Martinec |
| Introduction and historical notes |
| Hermitian matrix integral: saddle points and hyperellptic curves |
| The hermitian matrix model as a chiral CFT |
| Quasiclassical expansions: CFT on a hyperelliptic Riemann surface |
| Generalization to chains of random matrices |
| Preface.- Random Matrices and Number Theory |
| Introduction / 1： |
| Characteristic polynomials of random unitary matrices / 3： |
図書
