Affordable Access

Ergodic convergence rates of Markov processes--eigenvalues, inequalities and ergodic theory

Authors
  • Chen, Mu-Fa
Type
Published Article
Publication Date
Apr 23, 2003
Submission Date
Apr 23, 2003
Identifiers
arXiv ID: math/0304367
Source
arXiv
License
Unknown
External links

Abstract

This paper consists of four parts. In the first part, we explain what eigenvalues we are interested in and show the difficulties of the study on the first (non-trivial) eigenvalue through examples. In the second part, we present some (dual) variational formulas and explicit bounds for the first eigenvalue of Laplacian on Riemannian manifolds or Jacobi matrices (Markov chains). Here, a probabilistic approach--the coupling methods is adopted. In the third part, we introduce recent lower bounds of several basic inequalities; these are based on a generalization of Cheeger's approach which comes from Riemannian geometry. In the last part, a diagram of nine different types of ergodicity and a table of explicit criteria for them are presented. These criteria are motivated by the weighted Hardy inequality which comes from Harmonic analysis.

Report this publication

Statistics

Seen <100 times