@article{Liao2026, 
author = {Saixia Liao and Hanjun Zhang and Huasheng Li},
title = {Exponentially quasi-mixing ergodicity for symmetric Markov processes},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17009-17021},
keywords = {symmetric Markov process, intrinsic ultracontractivity, quasi-mixing limit, quasi-ergodicity, fractional quasi-ergodicity, mean-ratio quasi-ergodicity},
url = {https://www.sciopen.com/article/10.3934/math.2026696},
doi = {10.3934/math.2026696},
abstract = {In this paper, we focused on the quasi-mixing limits of symmetric Markov processes. Under mild assumptions, we proved that (intrinsic) ultracontractivity of the transition semigroup implied (uniformly) exponentially quasi-mixing ergodicity of its associated process. As a by-product, we demonstrated that the underlying process exhibited (uniformly) exponentially quasi-ergodicity, (uniformly) exponentially fractional quasi-ergodicity, and (uniformly) mean-ratio quasi-ergodicity being proportional to time.}
}