Quantitative Multiple pointwise convergence and effective multiple correlations

TL;DR

This paper establishes that effective multiple correlations lead to quantitative pointwise ergodic theorems for various systems, broadening understanding of convergence behaviors in ergodic theory.

Contribution

It demonstrates that effective multiple correlations imply quantitative multiple pointwise ergodic theorems across diverse dynamical systems.

Findings

Effective 2ℓ-multiple correlations imply quantitative ℓ-multiple pointwise ergodic theorems.

Applications include subgroup actions on homogeneous spaces and ergodic nilmanifold automorphisms.

Results cover systems like subshifts of finite type and Young towers.

Abstract

We show that effective $2\ell$-multiple correlations imply quantitative $\ell$-multiple pointwise ergodic theorems. The result has a wide class of applications which include subgroup actions on homogeneous spaces, ergodic nilmanifold automorphisms, subshifts of finite type and Young towers.