Limit law for some modified ergodic sums
Abstract
An example due to Erdos and Fortet shows that, for a lacunary sequence of integers (qn) and a trigonometric polynomial f, the asymptotic distribution of normalized sums of f(qk x) can be a mixture of gaussian laws. Here we give a generalization of their example interpreted as the limiting behavior of some modified ergodic sums in the framework of dynamical systems.
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