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Search: MSC category 37A05 ( Measure-preserving transformations )

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1. CJM Online first

Handelman, David
Nearly approximate transitivity (AT) for circulant matrices
By previous work of Giordano and the author, ergodic actions of $\mathbf Z$ (and other discrete groups) are completely classified measure-theoretically by their dimension space, a construction analogous to the dimension group used in C*-algebras and topological dynamics. Here we investigate how far from AT (approximately transitive) can actions be which derive from circulant (and related) matrices. It turns out not very: although non-AT actions can arise from this method of construction, under very modest additional conditions, ATness arises; in addition, if we drop the positivity requirement in the isomorphism of dimension spaces, then all these ergodic actions satisfy an analogue of AT. Many examples are provided.

Keywords:approximately transitive, ergodic transformation, circulant matrix, hemicirculant matrix, dimension space, matrix-valued random walk
Categories:37A05, 06F25, 28D05, 46B40, 60G50

2. CJM 2004 (vol 56 pp. 449)

Demeter, Ciprian
The Best Constants Associated with Some Weak Maximal Inequalities in Ergodic Theory
We introduce a new device of measuring the degree of the failure of convergence in the ergodic theorem along subsequences of integers. Relations with other types of bad behavior in ergodic theory and applications to weighted averages are also discussed.


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