# Statistics of patterns in typical cut and project sets

## TL;DR

This paper studies the statistical properties of patterns in typical cut and project sets, providing estimates on pattern frequency convergence and bounds on repetitivity and repulsivity, using discrepancy theory tools.

## Contribution

It offers new estimates and bounds for pattern frequencies, repetitivity, and repulsivity in cut and project sets, advancing understanding of their statistical structure.

## Key findings

- Estimates for convergence rates of pattern appearances
- Bounds for repetitivity functions
- Bounds for repulsivity functions

## Abstract

In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and repulsivity functions. The proofs use ideas and tools developed in discrepancy theory.