  Many systems exhibit a digit bias. For example, the first digit base 10 of
the Fibonacci numbers, or of $2^n$, equals 1 not 10% or 11% of the time, as one
would expect if all digits were equally likely, but about 30% of the time. This
phenomenon, known as Benford's Law, has many applications, ranging from
detecting tax fraud for the IRS to analyzing round-off errors in computer
science.
  The central question is determining which data sets follow Benford's law.
Inspired by natural processes such as particle decay, our work examines models
for the decomposition of conserved quantities. We prove that in many instances
the distribution of lengths of the resulting pieces converges to Benford
behavior as the number of divisions grow. The main difficulty is that the
resulting random variables are dependent, which we handle by a careful analysis
of the dependencies and tools from Fourier analysis to obtain quantified
convergence rates.
