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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1016/0749-8063(91)90183-X

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1572-9613

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Products of Random Matrices and Generalised Quantu

Authors: Alain Comtet Christophe Texier Yves Tourigny
Publish Date: 2010/06/18
Volume: 140, Issue: 3, Pages: 427-466
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Abstract

To every product of 2×2 matrices there corresponds a onedimensional Schrödinger equation whose potential consists of generalised point scatterers Products of random matrices are obtained by making these interactions and their positions random We exhibit a simple onedimensional quantum model corresponding to the most general product of matrices in SL2ℝ We use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms

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  2. Probabilistic Cellular Automata for Low-Temperature 2-d Ising Model
  3. Random Birth-and-Death Networks
  4. Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma
  5. On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices
  6. Symmetry of the Linearized Boltzmann Equation and Its Application
  7. Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov
  8. Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity
  9. Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System
  10. Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties
  11. New Horizons in Multidimensional Diffusion: The Lorentz Gas and the Riemann Hypothesis
  12. Clustering of Fermionic Truncated Expectation Values Via Functional Integration
  13. Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry–Mather Theory
  14. Revisiting the Glansdorff–Prigogine Criterion for Stability Within Irreversible Thermodynamics
  15. Ground State Energy of the One-Dimensional Discrete Random Schrödinger Operator with Bernoulli Potential
  16. A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths
  17. The More the Merrier?
  18. Non-equilibrium Phase Diagram for a Model with Coalescence, Evaporation and Deposition
  19. Real Spin Glasses Relax Slowly in the Shade of Hierarchical Trees
  20. Galton–Watson Trees with Vanishing Martingale Limit
  21. A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings
  22. Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians
  23. Dynamics of Infinitely Many Particles Mutually Interacting in Three Dimensions via a Bounded Superstable Long-Range Potential
  24. Statistical Mechanics of Nucleosomes Constrained by Higher-Order Chromatin Structure
  25. Large Deviations for the Branching Brownian Motion in Presence of Selection or Coalescence
  26. Clustering Bounds on n -Point Correlations for Unbounded Spin Systems
  27. Dissipative Diamagnetism—A Case Study for Equilibrium and Nonequilibrium Statistical Mechanics
  28. On the Transfer of Energy Towards Infinity in the Theory of Weak Turbulence for the Nonlinear Schrödinger Equation
  29. Finite-Time Fluctuations in the Degree Statistics of Growing Networks
  30. Exotic Ground States of Directional Pair Potentials via Collective-Density Variables
  31. Strong Asymmetric Coupling of Two Parallel Exclusion Processes
  32. Repeated Interaction Quantum Systems: Van Hove Limits and Asymptotic States
  33. On the Dynamics of the Glass Transition on Bethe Lattices
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  35. A Class of Random Walks in Reversible Dynamic Environments: Antisymmetry and Applications to the East Model
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  37. Rigorous Treatment of the Liquid-Vapor Transition in a Polydisperse System with Kac Interaction
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  40. Parameter Estimation for Multiscale Diffusions
  41. Onsager and Kaufman’s Calculation of the Spontaneous Magnetization of the Ising Model: II
  42. Injected Power Fluctuations in 1D Dissipative Systems
  43. Anomalies in Conductance and Localization Length of Disordered Ladders
  44. Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass
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