# Most random walks on nilpotent groups are mixing

Annales Polonici Mathematici (1992)

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

## Access Full Article

top## Abstract

top## How to cite

topR. 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

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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.