Mixing 𝑘-fold independent processes of zero entropy

Flaminio, L.

doi:10.1090/S0002-9939-1993-1154245-2

Mixing $k$-fold independent processes of zero entropy
HTML articles powered by AMS MathViewer

by L. Flaminio PDF

Proc. Amer. Math. Soc. 118 (1993), 1263-1269 Request permission

Abstract:

For each fixed $k$ we give a simple construction of a stochastic process $({X_n})$ which is mixing, has zero entropy, and such that any $k$-tuple of the ${X_n}$ are independent.

References

Richard C. Bradley, A stationary, pairwise independent, absolutely regular sequence for which the central limit theorem fails, Probab. Theory Related Fields 81 (1989), no. 1, 1–10. MR 981565, DOI 10.1007/BF00343735
S. Glasner and B. Weiss, A weakly mixing upside-down tower of isometric extensions, Ergodic Theory Dynam. Systems 1 (1981), no. 2, 151–157. MR 661816, DOI 10.1017/s0143385700009196
Svante Janson, Some pairwise independent sequences for which the central limit theorem fails, Stochastics 23 (1988), no. 4, 439–448. MR 943814, DOI 10.1080/17442508808833503
Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482
Brian Marcus, The horocycle flow is mixing of all degrees, Invent. Math. 46 (1978), no. 3, 201–209. MR 488168, DOI 10.1007/BF01390274
Donald S. Ornstein, On the root problem in ergodic theory, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 347–356. MR 0399415
Karl Petersen, Ergodic theory, Cambridge Studies in Advanced Mathematics, vol. 2, Cambridge University Press, Cambridge, 1983. MR 833286, DOI 10.1017/CBO9780511608728
Daniel J. Rudolph, $k$-fold mixing lifts to weakly mixing isometric extensions, Ergodic Theory Dynam. Systems 5 (1985), no. 3, 445–447. MR 805841, DOI 10.1017/S0143385700003060