  Recurrence quantification analysis is a method for measuring the complexity
of dynamical systems. Recurrence determinism is a fundamental characteristic of
it, closely related to correlation sum. In this paper, we study asymptotic
behavior of these quantities for interval maps. We show for which cases the
asymptotic correlation sum exists. An example of an interval map with zero
entropy and a point with the finite $\omega$-limit set for which the asymptotic
correlation sum does not exist is given. Moreover, we present formulas for
computation of the asymptotic correlation sum with respect to the cardinality
of the $\omega$-limit set or to the configuration of the intervals forming it,
respectively. We also show that for a not Li-Yorke chaotic (and hence zero
entropy) interval map, the limit of recurrence determinism as distance
threshold converges to zero can be strictly smaller than one.
