Semigroup inequalities, stochastic domination, Hardy's inequality, and strong ergodicity

$L^2$ 上紧强 Feller 半群的拟遍历性

Quasi-ergodicity of compact strong Feller semigroups on $L^2$

本文研究无限测度空间上非自伴紧强 Feller 半群的拟遍历性，通过热含量有限性与渐进一致基态支配刻画拟平稳测度唯一性，并应用于非局部 Schrödinger 算子。

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

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 fr…