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Uncoupling Measures and Eigenvalues of Stochastic Matrices

Published/Copyright: June 4, 2010
Journal of Applied Analysis
From the journal Journal of Applied Analysis Volume 4 Issue 2

Abstract

This paper gives bounds for the uncoupling measures of a stochastic matrix P in terms of its eigenvalues. The proofs are combinatorial. We use the Matrix–Tree Theorem which represents principal minors of I – P as sums of weights of directed forests.

Key words and phrases.: Stochastic matrices; nearly completely decomposable Markov chains; eigenvalues; uncoupling measures; directed forests; Matrix–Tree Theorem; numerical methods for linear systems
Received: 1998-06-15
Revised: 1998-09-28
Published Online: 2010-06-04
Published in Print: 1998-December

© Heldermann Verlag

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  1. Flows of Quantum Noise
  2. A Result Related to the Problem CN of Fremlin
  3. On Nonstationary Motion of a Compressible Barotropic Viscous Fluid with Boundary Slip Condition
  4. A New Generalization of Browder Fixed Point Theorem with Applications
  5. Oscillatory Solutions of a Class of Nonlinear Impulsive Differential Equations of First Order with Retarded Argument
  6. A New Version of the Multivalued Fatou Lemma
  7. Higher–Order Necessary Optimality Conditions for a Nonsmooth Extremum Problem
  8. Uncoupling Measures and Eigenvalues of Stochastic Matrices
  9. Mixed Coderivatives of Set–Valued Mappings in Variational Analysis
https://doi.org/10.1515/JAA.1998.259
Keywords for this article
Stochastic matrices; nearly completely decomposable Markov chains; eigenvalues; uncoupling measures; directed forests; Matrix–Tree Theorem; numerical methods for linear systems

Articles in the same Issue

  1. Flows of Quantum Noise
  2. A Result Related to the Problem CN of Fremlin
  3. On Nonstationary Motion of a Compressible Barotropic Viscous Fluid with Boundary Slip Condition
  4. A New Generalization of Browder Fixed Point Theorem with Applications
  5. Oscillatory Solutions of a Class of Nonlinear Impulsive Differential Equations of First Order with Retarded Argument
  6. A New Version of the Multivalued Fatou Lemma
  7. Higher–Order Necessary Optimality Conditions for a Nonsmooth Extremum Problem
  8. Uncoupling Measures and Eigenvalues of Stochastic Matrices
  9. Mixed Coderivatives of Set–Valued Mappings in Variational Analysis
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