### Betti, L, Durmić, I, McDonald, Z, Miller, JB and Miller, SJ (2023)

#### Benfordness of Measurements Resulting from Box Fragmentation

Preprint arXiv:2304.08335 [math.PR]; last accessed April 29, 2023.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

**Abstract:** We make progress on a conjecture made by [DM], which states that the d-dimensional frames of m-dimensional boxes resulting from a fragmentation process satisfy Benford's law for all 1≤d≤m. We provide a sufficient condition for Benford's law to be satisfied, namely that the maximum product of d sides is itself a Benford random variable. Motivated to produce an example of such a fragmentation process, we show that processes constructed from log-uniform proportion cuts satisfy the maximum criterion for d=1.

**Bibtex:**

```
@misc{,
title={Benfordness of Measurements Resulting from Box Fragmentation},
author={Livia Betti and Irfan Durmić and Zoe McDonald and Jack B. Miller and Steven J. Miller},
year={2023},
eprint={2304.08335},
archivePrefix={arXiv},
primaryClass={math.PR},
}
```

**Reference Type:** Preprint

**Subject Area(s):** Measure Theory, Probability Theory