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Central limit theorems for group actions which are exponentially mixing of all orders


Björklund, Michael; Gorodnik, Alexander (2020). Central limit theorems for group actions which are exponentially mixing of all orders. Journal d'analyse mathématique, 141(2):457-482.

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.

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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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Uncontrolled Keywords:Analysis, General Mathematics
Language:English
Date:1 September 2020
Deposited On:17 Dec 2020 15:35
Last Modified:12 Jan 2021 16:12
Publisher:Hebrew University Magnes Press
ISSN:0021-7670
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s11854-020-0106-7

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