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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

10.1016/0039-6028(85)90575-8

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1572-9613

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A Maximum Entropy Method Based on Piecewise Linear

Authors: Jiu Ding Congming Jin Noah H Rhee Aihui Zhou
Publish Date: 2011/09/29
Volume: 145, Issue: 6, Pages: 1620-1639
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Abstract

Let S01→01 be a nonsingular transformation such that the corresponding FrobeniusPerron operator P S L 101→L 101 has a stationary density f ∗ We propose a maximum entropy method based on piecewise linear functions for the numerical recovery of f ∗ An advantage of this new approximation approach over the maximum entropy method based on polynomial basis functions is that the system of nonlinear equations can be solved efficiently because when we apply Newton’s method the Jacobian matrices are positivedefinite and tridiagonal The numerical experiments show that the new maximum entropy method is more accurate than the Markov finite approximation method which also uses piecewise linear functions provided that the involved moments are known This is supported by the convergence rate analysis of the method

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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
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  7. Symmetry of the Linearized Boltzmann Equation and Its Application
  8. Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov
  9. Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity
  10. Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System
  11. Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties
  12. New Horizons in Multidimensional Diffusion: The Lorentz Gas and the Riemann Hypothesis
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  14. Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry–Mather Theory
  15. Revisiting the Glansdorff–Prigogine Criterion for Stability Within Irreversible Thermodynamics
  16. Ground State Energy of the One-Dimensional Discrete Random Schrödinger Operator with Bernoulli Potential
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