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Mat. Zametki, 1999, Volume 65, Issue 5, Pages 779–783 (Mi mz1109)  

This article is cited in 20 scientific papers (total in 20 papers)

Brief Communications

Ergodic theorems for the actions of a free group and a free semigroup

R. I. Grigorchuk

Steklov Mathematical Institute, Russian Academy of Sciences

DOI: https://doi.org/10.4213/mzm1109

Full text: PDF file (221 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 1999, 65:5, 654–657

Bibliographic databases:

Document Type: Article
Received: 25.12.1998

Citation: R. I. Grigorchuk, “Ergodic theorems for the actions of a free group and a free semigroup”, Mat. Zametki, 65:5 (1999), 779–783; Math. Notes, 65:5 (1999), 654–657

Citation in format AMSBIB
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\jour Math. Notes
\yr 1999
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Bufetov, “Ergodic theorems for actions of certain maps”, Russian Math. Surveys, 54:4 (1999), 835–836  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. I. Bufetov, “Operator Ergodic Theorems for Actions of Free Semigroups and Groups”, Funct. Anal. Appl., 34:4 (2000), 239–251  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. R. I. Grigorchuk, “An Ergodic Theorem for the Action of a Free Semigroup”, Proc. Steklov Inst. Math., 231 (2000), 113–127  mathnet  mathscinet  zmath
    4. Bufetov, AI, “Convergence of spherical averages for actions of free groups”, Annals of Mathematics, 155:3 (2002), 929  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Ball, K, “Factors of independent and identically distributed processes with non-amenable group actions”, Ergodic Theory and Dynamical Systems, 25 (2005), 711  crossref  mathscinet  zmath  isi  scopus  scopus
    6. G. Ya. Grabarnik, A. A. Katz, L. A. Shwartz, “On non-commutative ergodic type theorems for free finitely generated semigroups”, Vladikavk. matem. zhurn., 9:1 (2007), 38–47  mathnet  mathscinet  elib
    7. Hu, Y, “Maximal ergodic theorems for some group actions”, Journal of Functional Analysis, 254:5 (2008), 1282  crossref  mathscinet  zmath  isi  scopus  scopus
    8. A. I. Bufetov, A. V. Klimenko, M. I. Khristoforov, “Cesàro convergence of spherical averages for Markov groups and semigroups”, Russian Math. Surveys, 66:3 (2011), 633–634  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Bufetov A.I., Series C., “A Pointwise Ergodic Theorem for Fuchsian Groups”, Math. Proc. Camb. Philos. Soc., 151:Part 1 (2011), 145–159  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. A. I. Bufetov, A. V. Klimenko, “Maximal inequality and ergodic theorems for Markov groups”, Proc. Steklov Inst. Math., 277 (2012), 27–42  mathnet  crossref  mathscinet  isi
    11. Bufetov A., Klimenko A., “On Markov Operators and Ergodic Theorems for Group Actions”, Eur. J. Comb., 33:7, SI (2012), 1427–1443  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Bufetov A.I., Khristoforov M., Klimenko A., “Cesaro Convergence of Spherical Averages for Measure-Preserving Actions of Markov Semigroups and Groups”, Int. Math. Res. Notices, 2012, no. 21, 4797–4829  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    13. Bowen L., Nevo A., “Pointwise Ergodic Theorems Beyond Amenable Groups”, Ergod. Theory Dyn. Syst., 33:3 (2013), 777–820  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Bowen L., Nevo A., “A Horospherical Ratio Ergodic Theorem For Actions of Free Groups”, Group. Geom. Dyn., 8:2 (2014), 331–353  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Bowen L., Nevo A., “Von Neumann and Birkhoff Ergodic Theorems For Negatively Curved Groups”, Ann. Sci. Ec. Norm. Super., 48:5 (2015), 1113–1147  crossref  mathscinet  zmath  isi
    16. Grabarnik G.Ya., Katz A.A., Shwartz L., “a Note on Non-Commutative Ergodic Theorems For Actions of Hyperbolic Groups”, J. Math. Anal. Appl., 426:1 (2015), 624–633  crossref  mathscinet  zmath  isi  scopus  scopus
    17. Bowen L., Nevo A., “Amenable Equivalence Relations and the Construction of Ergodic Averages For Group Actions”, J. Anal. Math., 126:1 (2015), 359–388  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. Knauf A., “the Spectrum of An Adelic Markov Operator”, Indiana Univ. Math. J., 64:5 (2015), 1465–1512  crossref  mathscinet  zmath  isi  scopus  scopus
    19. V. Zh. Sakbaev, “On the law of large numbers for compositions of independent random semigroups”, Russian Math. (Iz. VUZ), 60:10 (2016), 72–76  mathnet  crossref  mathscinet  isi  elib  elib
    20. Bowen L., Bufetov A., Romaskevich O., “Mean convergence of Markovian spherical averages for measure-preserving actions of the free group”, Geod. Dedic., 181:1 (2016), 293–306  crossref  mathscinet  zmath  isi  scopus
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