# Hausdorff dimension of limsup sets of random rectangles in products of regular spaces

## TL;DR

This paper calculates the almost sure Hausdorff dimension of limsup sets formed by random rectangles in products of Ahlfors regular spaces, linking the dimension to the singular value function of the rectangles.

## Contribution

It introduces a method to determine the Hausdorff dimension of limsup sets of random rectangles in regular metric spaces using the singular value function.

## Key findings

- Hausdorff dimension expressed via singular value function
- Applicable to products of Ahlfors regular spaces
- Provides a probabilistic dimension formula

## Abstract

The almost sure Hausdorff dimension of the limsup set of randomly distributed rectangles in a product of Ahlfors regular metric spaces is computed in terms of the singular value function of the rectangles.