Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 1 ,pp. 72--88

SOME NEW EXAMPLES OF PAIRWISE INDEPENDENT RANDOM VARIABLES

By

ANDRZEJ KLOPOTOWSKI Universit\'e Paris XIII, Villetaneuse
and
JAMES B. ROBERTSON University of California, Santa Barbara

SUMMARY.We give some new examples of pairwise independent random variables. Special attention is paid to the problem of the existence of a dynamical system with simple Lebesgue spectrum.

AMS (1991) subject classification.Primary 60A05, 60G10; secondary 47A35, 28D20.

Key words and phrases. Stationary process, pairwise independence, m--dependence, Markov chain, dynamical system, simple Lebesgue spectrum.

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