Pacific Journal of Mathematics

Strong approximate transitivity, polynomial growth, and spread out random walks on locally compact groups.

Wojciech Jaworski

Article information

Source
Pacific J. Math., Volume 170, Number 2 (1995), 517-533.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102370883

Mathematical Reviews number (MathSciNet)
MR1363877

Zentralblatt MATH identifier
0849.60007

Subjects
Primary: 43A05: Measures on groups and semigroups, etc.
Secondary: 22D99: None of the above, but in this section

Citation

Jaworski, Wojciech. Strong approximate transitivity, polynomial growth, and spread out random walks on locally compact groups. Pacific J. Math. 170 (1995), no. 2, 517--533. https://projecteuclid.org/euclid.pjm/1102370883


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References

  • [1] A. Avez, Harmonic functions on groups,In: Cahen and Flato (eds.): Differential geometry and Relativity, Reidel, Dordrecht 1976, 27-32.
  • [2] R. Azencott, Espaces de Poisson des groupes localement compacts, Lecture Notes in Mathematics., vol 148, Springer, Berlin 1970.
  • [3] N. Bourbaki, Elements de mathematique. Groupes et algebres de Lie, Chaps. VII, VIII, Hermann, Paris 1975.
  • [4] E.G. Effros, Transformation groups and C*-algebras, Annals of Math., 81 (1965), 38-55.
  • [5] H. Furstenberg, Boundary theory and stochastic processes on homogeneous spaces, Proc. Sympos. Pure Math., vol 26: Harmonic analysis on homogeneous spaces, AMS, Providence, R.I. 1973, 193-229.
  • [6] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. I.H.E.S., 53 (1981), 53-73.
  • [7] Y. Guivarc'h, Croissance polynomiale et periodes des fonctions harmoni-ques, Bull. Soc. Math. France, 101 (1973), 333-379.
  • [8] H. Heyer, Probability measures on locally compact groups, Springer, Berlin 1977.
  • [9] W. Jaworski, Strongly approximately transitive group actions, theChoquet-Deny theorem, and polynomial growth, Pacific J. Math., 165 (1994), 115-129.
  • [10] W. Jaworski, unpublished manuscript.
  • [11] W. Jaworski, Poisson and Furstenberg boundaries of random walks, C.R. Math. Rep. Acad. Sci. Canada, XIII (1991), 279-284.
  • [12] J.W. Jenkins, Folner}s condition for exponentially bounded groups, Math. Scand., 35 (1974), 165-174.
  • [13] J.W. Jenkins, Growth of connected locally compact groups, J. Punct. Analysis, 12 (1973), 113-127.
  • [14] M.I. Kargapolov and Ju.I. Merzljakov, Fundamentals of the theory of groups, Springer, New York 1979.
  • [15] V. Losert, On the structure of groups with polynomial growth, Math. Z., 195 (1987), 195-217.
  • [16] G.W. Mackey, Point realizations of transformationgroups, Illinois J. Math., 6 (1962), 327-335.
  • [17] J. Neveu, Mathematical foundations of the calculus of probability, Holden-Day, San Francisco 1965.
  • [18] O.A. Nielsen, Direct integral theory, Lecture notes in pure and applied math., vol.
  • [19] A.L.T. Paterson, Amenability, AMS, Providence 1988.
  • [20] D. Revuz, Markov chains, North-Holland, Amsterdam 1975.
  • [21] A. Raugi, Fonctions harmoniques sur les groupes localement compacts a base de- nombrable, Bull. Soc. Math. France, Memoire, 54 (1977), 5-118.
  • [22] J.M. Rosenblatt, Invariant measures and growth conditions, Trans. Amer. Math. Soc, 193 (1974), 33-35.
  • [23] J.M. Rosenblatt, Ergodic and mixing random walks on locally compact groups, Math. Ann., 257 (1981), 31-42.
  • [24] V.S. Varadarajan, Groups of automorphisms of Borel spaces, Trans. Amer. Math. Soc, 109 (1963), 191-220.
  • [25] V.S. Varadarajan, Geometry of quantum theory, Vol. 2, Van Nostrand 1970.
  • [26] R.J. Zimmer, Amenable ergodic groups actions and an application to Poisson bound- aries of random walks, J. Funct. Analysis, 27 (1978), 350-372.
  • [27] R.J. Zimmer, Ergodic theory and semisimple groups, Birkhauser, Boston 1984.