Effective Multiple Equidistribution of Translated Measures

Journal article, 2023

We study the joint distributions of translated measures supported on periodic orbits that are expanded by subgroups of diagonal matrices and generalize (special cases) of previous results of Kleinbock-Margulis, Dabbs-Kelly-Li, and Shi. More specifically, we establish quantitative estimates on higher-order correlations for measures with low regularities and derive error terms that only depend on the distances between translations.