Decorrelation estimates for translated measures under diagonal flows
Year: 2025
Type: article
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.
Source: Journal of Modern Dynamics
DOI: 10.3934/jmd.2025007
Institutions: University of Michigan, University of Zurich
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411668527