A Strong Mixing Condition and a Central Limit Theorem on Compact Groups

A Central Limit Theorem and a Strong Mixing Condition.

The Central Limit Theorem for uniformly strong mixing measures

The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is finite). In this paper we prove that the measure of cylinder sets are lognormally distributed for strongly mixing systems and infinite partitions and show that the ...

Mixing Automorphisms of Compact Groups and a Theorem of Schlickewei

We prove that every mixing Z-action by automorphisms of a compact, connected, abelian group is mixing of all orders.

A Central Limit Theorem on Heisenberg Type Groups. Ii

We present a Liapounov type central limit theorem for random variables associated to a commutative Banach algebra of "radial" measures on Heisenberg type groups. This theorem improves on a result presented by the author in Proc. Amer. Math. Soc. 113 (1991), 529-536. 0. Introduction In [Oh] we introduced a commutative algebra of "radial", bounded, Borel measures on Heisenberg type groups (H-type...

A Central Limit Theorem on Heisenberg Type Groups

Heisenberg type groups are a class of 2-step nilpotent Lie groups which have many similarities with Heisenberg groups. In this paper we consider a commutative Banach algebra of radial, bounded, Borel measures on such groups and prove a central limit theorem for measures in this algebra satisfying suitable growth conditions. 0. Introduction One of the main themes in the area of nilpotent Lie gro...