An invitation to Fibonacci digits
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.
math.HO↗
arXiv subjects
Zoe McDonald
Publications and source records attributed to Zoe McDonald.
A stochastic combustion model with thresholds on trees
Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any dormant particles there become active. For this process on infinite $d$-ary trees, we show that total root visits undergoes a phase transition.
math.PR↗
Benfordness of Measurements Resulting from Box Fragmentation
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 $1 \leq d \leq m$. 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 $d=1$.
math.PR↗