Most random walks on nilpotent groups are mixing

R. Rębowski

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 3, page 265-268
  • ISSN: 0066-2216

Abstract

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Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.

How to cite

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R. Rębowski. "Most random walks on nilpotent groups are mixing." Annales Polonici Mathematici 57.3 (1992): 265-268. <http://eudml.org/doc/275943>.

@article{R1992,
abstract = {Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.},
author = {R. Rębowski},
journal = {Annales Polonici Mathematici},
keywords = {stochastic operator; convolution operator; random walk; norm completely mixing; nilpotent group; second countable locally compact group with a left Haar measure; norm completely mixing random walks; stochastic convolution operators; nilpotent groups; Poisson spaces},
language = {eng},
number = {3},
pages = {265-268},
title = {Most random walks on nilpotent groups are mixing},
url = {http://eudml.org/doc/275943},
volume = {57},
year = {1992},
}

TY - JOUR
AU - R. Rębowski
TI - Most random walks on nilpotent groups are mixing
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 3
SP - 265
EP - 268
AB - Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.
LA - eng
KW - stochastic operator; convolution operator; random walk; norm completely mixing; nilpotent group; second countable locally compact group with a left Haar measure; norm completely mixing random walks; stochastic convolution operators; nilpotent groups; Poisson spaces
UR - http://eudml.org/doc/275943
ER -

References

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  1. [1] R. Azencott, Espaces de Poisson des groupes localement compacts, Lecture Notes in Math. 148, Springer, Berlin 1970. Zbl0239.60008
  2. [2] W. Bartoszek, On the residuality of mixing by convolution probabilities, preprint. Zbl0785.43001
  3. [3] S. Glasner, On Choquet-Deny measures, Ann. Inst. Henri Poincaré 12 (1976), 1-10. Zbl0349.60006
  4. [4] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. 2, Springer, Berlin 1970. Zbl0213.40103
  5. [5] H. Heyer, Probability Measures on Locally Compact Groups, Springer, Berlin 1977. Zbl0376.60002
  6. [6] A. Iwanik and R. Rębowski, Structure of mixing and category of complete mixing for stochastic operators, Ann. Polon. Math. 56 (1992), 233-242. Zbl0786.47004
  7. [7] B. Jamison and S. Orey, Markov chains recurrent in the sense of Harris, Z. Wahrsch. Verw. Gebiete 8 (1967), 41-48. Zbl0153.19802
  8. [8] D. Revuz, Markov Chains, North-Holland Math. Library, 1975. 
  9. [9] J. Rosenblatt, Ergodic and mixing random walks on locally compact groups, Math. Ann. 257 (1981), 31-42. Zbl0451.60011

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