Abstract
Inspired by the multiple recurrence and multiple ergodic theorems for measure preserving systems, we discuss an analogous question for measure preserving semigroups. In this note, we deal with the symmetric semigroups associated to reversible Markov chains.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bergelson, V., Leibman, A. Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. Journal Amer. Math. Soc., 9: 725–753 (1996)
Erdős, P., Turán, P. On some sequences of integers. J. London Math. Soc., 11: 261–264 (1936)
Furstenberg, H. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. d’Analyse Math., 31: 204–256 (1977)
Host, B., Kra. B. Nonconventional ergodic averages and nilmanifolds. Ann. of Math., (1)161 (2): 397–488 (2005)
Host, B., Kra. B. Convergence of polynomial ergodic averages, probability in mathematics. Israel J. Math., 149: 1–19 (2005)
Kifer, Y. Nonconventional limit theorems. Probab. Theory Relat. Fields, 148: 71–106 (2010)
Szemerédi, E. On sets of integers containing no k elements in arithmetic progression. Acta Arith., 27: 199–245 (1975)
Yoshida, K. Functional Analysis. Springer-Verlag, New York, 1971
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (No. 11431014, no. 11688101), AMSS research grant (No. Y129161ZZ1), and Key Laboratory of Random Complex Structures and Data, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (No. 2008DP173182).
Rights and permissions
About this article
Cite this article
Liu, Y. Multiple Ergodicity For Reversible Markov Chains. Acta Math. Appl. Sin. Engl. Ser. 34, 863–868 (2018). https://doi.org/10.1007/s10255-018-0779-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-018-0779-1