Decorrelation estimates for translated measures under diagonal flows

2023/11/20 by Michael Björklund, Reynold Fregoli, Björklund, Michael +3
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2311.11942

openalex publication_date 2023/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Λ_B translated by a multi-parameter semigroup a(t). We establish quantitative decorrelation estimates for measures supported on leaves a(t)Λ_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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