http://www.gbv.de/dms/hebis-darmstadt/toc/113948433.pdf

The Problem of Integrable Discretization: Hamiltonian Approach

Collisions of Calogero-Moser particles and an adelic Grassmannian

We give a review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains.

The physics and mathematics of Calogero particles

We quantize the spin Calogero-Moser model in theR-matrix formalism. The quantumR-matrix of the model is dynamical. ThisR-matrix has already appeared in Gervais-Neveu's quantization of Toda field theory and in Felder's quantization of the Knizhnik-Zamolodchikov-Bernard equation.

/pdf/the-gervais-neveu-felder-equation-and-the-quantum-calogero-kr46xiytgp.pdf

The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems

Preface- Random Matrices and Number Theory 1 Introduction 2 3 Characteristic polynomials of random unitary matrices 4 Other compact groups 5 Families of L-functions and Symmetry 6 Asymptotic expansions References JP Keating- 2D Quantum Gravity, Matrix Models and Graph Combinatorics 1 Introduction 2 Matrix models for 2D quantum gravity The one-matrix model I: large N limit and the enumeration of planar graphs 4 The trees behind the graphs 5 The one-matrix model II: topological expansions and quantum gravity 6 The combinatorics beyond matrix models: geodesic distance in planar graphs 7 Planar graphs as spatial branching processes 8 Conclusion P Di Francesco- Eigenvalue Dynamics, Follytons and Large N Limits of Matrices References J Arnlind, J Hoppe- Random Matrices and Supersymmetry in Disordered Systems Supersymmetry method 2 Wave functions fluctuations in a finite volume Multifractality Recent and possible future developments Summary Acknowledgements References KB Efetov- Hydrodynamics of Correlated Systems 1 Introduction 2 Instanton or rare fluctuation method 3 Hydrodynamic approach 4 Linearized hydrodynamics or bosonization 5 EFP through an asymptotics of the solution 6 Free fermions 7 Calogero-Sutherland model 8 Free fermions on the lattice 9 Conclusion Acknowledgements Appendix: Hydrodynamic approach to non-Galilean invariant systems Appendix: Exact results for EFP in some integrable models References AG Abanov- QCD, Chiral Random Matrix Theory and Integrability 1 Summary 2 Introduction 3 QCD 4 The Dirac Spectrum in QCD 5 Low Energy Limit of QCD 6 Chiral RMT and the QCD Dirac Spectrum 7 Integrability and the QCD Partition Function 8 QCD at Finite Baryon Density 9 Full QCD at Nonzero Chemical Potential 10 Conclusions Acknowledgements References JJ M Verbaarschot- Euclidan Random Matrices: Solved and Open Problems 1 Introduction 2 Basic definitions 3 Physical motivations 4 Field theory 5 The simplest case 6 Phonnos References G Parisi- Matrix Models and Growth Processes 1 Introduction 2 Some ensembles of random matrices with complex eigenvalues 3 Exact results at finite N 4 Large N limit 5 The matrix model as a growth problem References A Zabrodin- Matrix Models and Topological Strings 1 Introduction 2 Matrix models 3 Type B topological strings and matrix models 4 Type A topological strings, Chern-Simons theory and matrix models M Marino- Matrix Models of Moduli Space 1 Introduction 2 Moduli Space of Riemann Surfaces and its Topology 3 Quadratic Differentials and Fatgraphs 4 The Penner model 5 Penner Model and Matrix Gamma Function 6 The Kontsevich Model 7 Applications to String Theory 8 Conclusions References S Mukhi- Matrix Models and 2D String Theory 1 Introduction 2 An overview of string theory 3 Strings in D-dimensional spacetime 4 Discretized surfaces and 2D string theory 5 An overview of observables 6 Sample calculation: the disk one-point function 7 Worldsheet description of matrix eigenvalues 8 Further results 9 Open problems References EJ Martinec- Matrix Models as Conformal Field Theories 1 Introduction and historical notes 2 Hermitian matrix integral: saddle points and hyperellptic curves 3 The hermitian matrix model as a chiral CFT 4 Quasiclassical expansions: CFT on a hyperelliptic Riemann surface 5 Generalization to chains of random matrices References IK Kostov-

/pdf/applications-of-random-matrices-in-physics-3m7y9h00e3.pdf

Applications of random matrices in physics

A generalisation of the Calogero-Moser system

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A generalisation of the Calogero-Moser system