Applications of Random Matrices in Physics (eBook)

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2006
X, 514 Seiten
Springer Netherlands (Verlag)
978-1-4020-4531-8 (ISBN)

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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.
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.

Contents 6
Preface 10
RANDOM MATRICES AND NUMBER THEORY 12
2D QUANTUM GRAVITY, MATRIX MODELS AND GRAPH COMBINATORICS 44
EIGENVALUE DYNAMICS, FOLLYTONS AND LARGEN LIMITS OF MATRICES 100
RANDOM MATRICES AND SUPERSYMMETRY IN DISORDERED SYSTEMS 106
HYDRODYNAMICS OF CORRELATED SYSTEMS 149
QCD, CHIRAL RANDOM MATRIX THEORYAND INTEGRABILITY 172
EUCLIDEAN RANDOMMATRICES: SOLVEDAND OPEN PROBLEMS 227
MATRIX MODELS AND GROWTH PROCESSES: FROM VISCOUS FLOWS TO THE QUANTUM HALL EFFECT 269
MATRIX MODELS AND TOPOLOGICAL STRINGS 327
MATRIX MODELS OF MODULI SPACE 387
MATRIX MODELS AND 2D STRING THEORY 410
MATRIX MODELS AS CONFORMALFIELD THEORIES 465
LARGE N ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS FROM INTEGRABILITY TO ALGEBRAIC GEOMETRY 494

Erscheint lt. Verlag 3.7.2006
Reihe/Serie Nato Science Series II:
NATO Science Series II: Mathematics, Physics and Chemistry
NATO Science Series II: Mathematics, Physics and Chemistry
Zusatzinfo X, 510 p.
Verlagsort Dordrecht
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Statistik
Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Naturwissenschaften Physik / Astronomie Theoretische Physik
Technik
Schlagworte Baryon • Chemistry • Correlation • Mathematics • NATO • Observable • Physics • Potential • Science • Series II
ISBN-10 1-4020-4531-X / 140204531X
ISBN-13 978-1-4020-4531-8 / 9781402045318
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