Exponentially quasi-mixing ergodicity for symmetric Markov processes

Saixia Liao; Hanjun Zhang; Huasheng Li; Saixia Liao; Hanjun Zhang; Huasheng Li

doi:10.3934/math.2026696

AIMS Mathematics

2026, Volume 11, Issue 6: 17009-17021. doi: 10.3934/math.2026696

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Research article

Exponentially quasi-mixing ergodicity for symmetric Markov processes

1.
School of Mathematical Sciences, Changsha Normal University, Changsha, Hunan 410100, China
2.
School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
3.
School of Mathematics and Statistics, Hainan University, Haikou, Hainan 570000, China

Received: 17 March 2026 Revised: 01 June 2026 Accepted: 08 June 2026 Published: 12 June 2026
MSC : 37A30, 47D07, 60J25, 60J35

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.
- symmetric Markov process,
- intrinsic ultracontractivity,
- quasi-mixing limit,
- quasi-ergodicity,
- fractional quasi-ergodicity,
- mean-ratio quasi-ergodicity
Citation: Saixia Liao, Hanjun Zhang, Huasheng Li. Exponentially quasi-mixing ergodicity for symmetric Markov processes[J]. AIMS Mathematics, 2026, 11(6): 17009-17021. doi: 10.3934/math.2026696

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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.

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