Effective multiple equidistribution of translated measures

TL;DR

This paper investigates the joint distributions of translated measures on expanded leaves, providing quantitative estimates on higher-order correlations with error terms based on translation distances, generalizing prior results.

Contribution

It introduces new quantitative estimates for higher-order correlations of translated measures with low regularity, extending previous work in the field.

Findings

Established bounds on higher-order correlations.

Derived error terms depending on translation distances.

Generalized previous equidistribution results.

Abstract

We study the joint distributions of translated measures supported on leaves which are expanded by subgroups of diagonal matrices and generalize 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 which only depend on the distances between translations.