with respect to an integer
base 
satisfies a central limit theorem on the set of integers
with mean and variance proportional to 
. (Interestingly
this is also true on the set of prime numbers 
as well as on
polynomial sequences.)
The statistical behaviour of digital expansions plays a role in the
analysis of several algorithms (divide-and-conquer strategies such as
mergesort, traffic cutback, determination of sets with maximal number
of interconnecting edges, RSA, ...). For example, it is well known
that the sum-of-digits function with respect to an integer
base satisfies a central limit theorem on the set of integers
with mean and variance proportional to . (Interestingly
this is also true on the set of prime numbers as well as on
polynomial sequences.)
The purpose of this talk is to demonstrate a general method for determining limiting distributions of that kind which also works for more general digital expansions, e.g. those with respect to a linear recurrence such as the Zeckendorf expansion (based on the Fibonacci numbers). The problem consists mostly in determining the value of a digit without using the greedy algorithm. For a large class of recurrences, this can be done by using Rauzy fractals. Finally, the central limit theorem is then an (almost automatic) consequence of estimates for exponential sums.