A countably-valued sleeping stockbroker process (Q1337942)

The authors exhibit a stationary countably-valued process \(\{V_ n\}^ \infty_{-\infty}\) which is deterministic, but which is nondeterministic in the sense that whenever \(\dots n_{-2} < n_{-1} < n_ 0 < n_ 1 < \dots\) are indices with no two consecutive, then \(\{V_{n_ i} : i \in \mathbb{Z}\}\) is an independent process. This answers a question of \textit{J. L. King} [Am. Math. Mon. 99, No. 4, 335-338 (1992; Zbl 0754.60032)]. The construction uses Haar measure on finite groups and a ``look-ahead'' condition, and has the additional property that although \(n \mapsto V_ n\) is deterministic, its time-reversal \(n \mapsto V_{-n}\) is not.