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Book Freeshipping Applications Of Random Matrices In Physics Photo-engraving Edition

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Applications of Random Matrices in Physics (Photo-engraving Edition), by Brezin.E., English, Hardcover,


Product Details

Author Brezin.E.

Press Science Press

Isbn 7030226267/9787030226266

Publication Date Aug 2008

Pages 513

Size 16K

Edition First

Cover Hardcover

Language English

Page material gelatine plate paper

Product Description:

This book is composed by eminent scholar in physics, expounding relevant theoretic knowledge. This book can be a reference to Graduate students who are interested in Random Matrices in Physics and the scientific researchers.



Random Matrices and Number Theory

J.P. Keating

1 Introduction

2 ζ(1/2+it)and logζ(1/2+it)

3 Characteristic polynomials of random unitary matrices

4 Other compact groups

5 Families of L-functions and symmetry

6 Asymptotic expansions


2D Quantum Gravity, Matrix Models and Graph Combinatorics

P. Di Francesco

1 Introduction

2 Matrix models for 2D quantum gravity

3 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 58

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

Joakim Arnlind, Jens Hoppe


Random Matrices and Supersymmetry in Disordered Systems

K.B. Efetov

1 Supersymmetry method

2 Wave functions fluctuations in a finite volume. Multifractality

3 Recent and possible future developments

4 Summary



Hydrodynamics of Correlated Systems

Alexander G.Abanoy

1 Introduction

2 Instanton or rare fluctuation method

3 Hydrodynam ic approach

4 Linearized hydrodynamics or bosoflization

5 EFP through an asymptotics of the solution

6 Free fermions

7 Calogero-Sutherland model

8 Free fermions on the lattice

9 Conclusion


Appendix:Hydrodynamic approach to non-Galilean invariant systems

Appendix:Exact results for EFP in some integrable models


QCD,Chiral Random Matrix Theory and Integrability


1 Summarv

2 IntrodUCtion

3 ocd

4 The Dirac spectrum in QCD

5 Low eflergy limit of QCD

6 Chiral RMT and the QCD Dirac spectrum

7 Integrability and the QCD partition function

8 QCD at fin ite baryon density

9 Full QCD at nonzero chemical potential

10 Conclusions



EUClidean Random Matrices:SOlved and Open Problems

Giorgio Parisi

1 Introduction

2 Basic definitions

3 Physical motivations

4 Field theory

5 The simplest case

6 Phonons


Matrix Models and Growth Processes3


1 Introduction

2 Some ensembles of random matrices with cornplex eigenvalues

3 Exact results at finite N

4 Large N limit

5 The matrix model as a growth problem


Matrix Models and Topological Strings

Marcos Marino

1 Introduction

2 Matrix models

3 Type B topological strings and matrix models

4 Type A topological strings, Chern-Simons theory and matrix models 366


Matrix Models of Moduli Space

Sunil Mukhi

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


Matrix Models and 2D String Theory

Emil J. Martinec

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


Matrix Models as Conformal Field Theories

Ivan K. Kostov

1 Introduction and historical notes

2 Hermitian matrix integral: saddle points and hyperelliptic curves

3 The hermitian matrix model as a chiral CFT

4 Quasiclassical expansion: CFT on a hyperelliptic Riemann surface

5 Generalization to chains of random matrices


Large N Asymptotics of Orthogonal Polynomials from Integrability to Algebraic Geometry

B. Eynard

1 Introduction

2 Definitions

3 Orthogonal polynomials

4 Differential equations and integrability

5 Riemann-Hilbert problems and isomonodromies

6 WKB-like asymptotics and spectral curve

7 Orthogonal polynomials as matrix integrals

8 Computation of derivatives of F(0)

9 Saddle point method

10 Solution of the saddlepoint equation

11 Asymptotics of orthogonal polynomials

12 Conclusion


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