Benfordness of Measurements Resulting from Box Fragmentation

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 $1\le d\le m$. 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 $d=1$.

13 pages, 3 figures, to be submitted to the Journal of Statistical Theory and Practice