Applications of Random Matrices in Physics. 1st ed. 2006

種類:

電子ブック

責任表示:

edited by Édouard Brezin, Vladimir Kazakov, Didina Serban, Paul Wiegmann, Anton Zabrodin

出版情報:

Dordrecht : Springer Netherlands : Imprint: Springer, 2006

著者名:

Brezin, Édouard.

Kazakov, Vladimir.

Serban, Didina.

Wiegmann, Paul.

Zabrodin, Anton.

SpringerLink (Online service)

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シリーズ名:

NATO Science Series II: Mathematics, Physics and Chemistry, Mathematics, Physics and Chemistry ; 221

ISBN:

9781402045318 [140204531X]    

注記:

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 -- 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 -- Eigenvalue Dynamics, Follytons and Large N Limits of Matrices. References -- 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 -- Hydrodynamics of Correlated Systems. 1. Intr
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.

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