Harmonic models and Bernoullicity

We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left-orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements in any left-orderable group. For many of our examples, the acting group is amenable so these actions are Bernoulli (and not just a factor of a Bernoulli), but there is no obvious Bernoulli partition.

BERNOULLI PARTITION-EQUIVALENCE OF INTERMITTENT NEURONAL DISCHARGE PATTERNS

The binary partition of the range of values for a series of interspike intervals necessary to generate the growth rate of the longest run equivalent to that observed in a Bernoulli, fair coin sequence was found to discriminate three classes of intermittently firing brain stem neurons more clearly than either the higher statistical moments or the leading Lyapunov exponent.