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arXiv · 2311.11942

Decorrelation estimates for translated measures under diagonal flows

Michael Björklund·Reynold Fregoli·Alexander Gorodnik
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Abstract

A profound link between Homogeneous Dynamics and Diophantine Approximation is based on an observation that Diophantine properties of a real matrix $B$ are encoded by the corresponding lattice $\Lambda_B$ translated by a multi-parameter semigroup $a(t)$. We establish quantitative decorrelation estimates for measures supported on leaves $a(t)\Lambda_B$ with the error terms depending only on the minimum of the pairwise distances between the parameters. The proof involves a careful analysis of the translated measures in the products of the spaces of unimodular lattices and establishes quantitative equidistributions to measures supported on various intermediate homogeneous subspaces.

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Michael Björklund, Reynold Fregoli, Alexander Gorodnik. 2023-11-20. Decorrelation estimates for translated measures under diagonal flows. https://arxiv.org/abs/2311.11942

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