  A fundamental algorithm for selecting ranks from a finite subset of an
ordered set is Radix Selection. This algorithm requires the data to be given as
strings of symbols over an ordered alphabet, e.g., binary expansions of real
numbers. Its complexity is measured by the number of symbols that have to be
read. In this paper the model of independent data identically generated from a
Markov chain is considered. The complexity is studied as a stochastic process
indexed by the set of infinite strings over the given alphabet. The orders of
mean and variance of the complexity and, after normalization, a limit theorem
with a centered Gaussian process as limit are derived. This implies an analysis
for two standard models for the ranks: uniformly chosen ranks, also called
grand averages, and the worst case rank complexities which are of interest in
computer science. For uniform data and the asymmetric Bernoulli model (i.e.
memoryless sources), we also find weak convergence for the normalized process
of complexities when indexed by the ranks while for more general Markov sources
these processes are not tight under the standard normalizations.
