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arXiv · 1706.09167

Central Limit Theorems for group actions which are exponentially mixing of all orders

Michael Björklund·Alexander Gorodnik
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Abstract

In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie groups. Our proof uses a novel relativization of the classical method of cumulants, which should be of independent interest. As a sample application of our techniques, we show that the CLT holds along lacunary samples of the horocycle flow on finite-area hyperbolic surfaces applied to any smooth compactly supported function.

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Michael Björklund, Alexander Gorodnik. 2017-06-28. Central Limit Theorems for group actions which are exponentially mixing of all orders. https://arxiv.org/abs/1706.09167

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