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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Open Access
Research Article
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AIMS Mathematics 2026, 11(6): 17009-17021
Published: 15 June 2026
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