Most random walks on nilpotent groups are mixing

• Autorzy: R. Rębowski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

stochastic operator; convolution operator; random walk; norm completely mixing; nilpotent group

Kategorie tematyczne

• 47A35: Ergodic theory
• 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
• 22D40: Ergodic theory on groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 3
• Strony: 265-268

Daty

wydano

1992

otrzymano

1991-11-15

poprawiono

1992-05-20

Twórcy

autor

R. Rębowski

• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• [1] R. Azencott, Espaces de Poisson des groupes localement compacts, Lecture Notes in Math. 148, Springer, Berlin 1970.
• [2] W. Bartoszek, On the residuality of mixing by convolution probabilities, preprint.
• [3] S. Glasner, On Choquet-Deny measures, Ann. Inst. Henri Poincaré 12 (1976), 1-10.
• [4] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. 2, Springer, Berlin 1970.
• [5] H. Heyer, Probability Measures on Locally Compact Groups, Springer, Berlin 1977.
• [6] A. Iwanik and R. Rębowski, Structure of mixing and category of complete mixing for stochastic operators, Ann. Polon. Math. 56 (1992), 233-242.
• [7] B. Jamison and S. Orey, Markov chains recurrent in the sense of Harris, Z. Wahrsch. Verw. Gebiete 8 (1967), 41-48.
• [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.