Products of random matrices in statistical physics

摘要: I Background.- 1. Why Study Random Matrices?.- 1.1 Statistics of the Eigenvalues Matrices.- 1.1.1 Nuclear Physics.- 1.1.2 Stability Large Ecosystems.- 1.1.3 Disordered Harmonic Solids.- 1.2 Products Matrices in Chaotic and Systems.- 1.2.1 1.2.2 1.3 Some Remarks on Calculation Lyapunov Exponent PRM.- 2. Exponents for 2.1 Asymptotic Limits: Furstenberg Oseledec Theorems.- 2.2 Generalized Exponents.- 2.3 Numerical Methods Computation 2.4 Analytic Results.- 2.4.1 Weak Disorder Expansion.- 2.4.2 Replica Trick.- 2.4.3 Microcanonical Method.- II Applications.- 3. Dynamical 3.1 Deterministic Chaos.- 3.1.1 The Independent RM Approximation.- 3.1.2 Approximation: Perturbative Approach.- 3.1.3 Beyond 3.2 CLE High Dimensional 4. 4.1 One-Dimensional Ising Model Transfer 4.2 Models.- 4.2.1 Chain with Field.- 4.2.2 Coupling.- 4.3 Free Energy Fluctuations.- 4.4 Correlation Functions 4.5 Two-and Three-Dimensional 5. Localization.- 5.1 Localization 5.1.1 Exponential Growth Localization: Borland Conjecture.- 5.1.2 Density States 5.1.3 Conductivity Exponents: Landauer Formula.- 5.2 PRMs 5.2.1 5.2.2 Trick 5.2.3 Lengths.- 5.2.4 Potentials Extended States.- 5.3 Two Three Dimensions.- 5.4 Maximum Entropy Approach to Conductance III Miscellany.- 6. Other 6.1 Propagation Light Media.- 6.1.1 Media Optical Index.- 6.1.2 Randomly Deformed Waveguide.- 6.2 Magnetic Dynamos.- 6.3 Image Compression.- 6.3.1 Iterated Function System.- 6.3.2 Determination IFS Code 7. Appendices.- 7.1 Real Asymmetric 7.2 Program Spectrum.- 7.3 Poincare Section.- 7.4 Markov Shannon Entropy.- 7.5 Kolmogorov-Sinai Topological Entropies.- 7.6 Fractal Dimensions Multifractals.- 7.7 Correlated Potentials.- References.