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arXiv · 1001.4862

Limit law for some modified ergodic sums

Jean-Pierre Conze·Stéphane Le Borgne
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Abstract

An example due to Erdos and Fortet shows that, for a lacunary sequence of integers (q_n) and a trigonometric polynomial f, the asymptotic distribution of normalized sums of f(q_k 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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Jean-Pierre Conze, Stéphane Le Borgne. 2010-01-27. Limit law for some modified ergodic sums. https://arxiv.org/abs/1001.4862

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