  In their recent paper [8], G.Hata and the fourth author first gave an example
of random iterations of two piecewise linear interval maps without
(deterministic) indifferent periodic points for which the arcsine law -- a
characterization of intermittent dynamics in infinite ergodic theory -- holds.
The key in the proof of the result is the existence of a Markov partition
preserved by each interval maps. In the present paper, we give a class of
random iterations of two interval maps without indifferent periodic points but
satisfying the arcsine law, by introducing a concept of core random dynamics.
As applications, we show that the generalized arcsine law holds for generalized
Hata-Yano maps and piecewise linear versions of Gharaei-Homburg maps, both of
which do not have a Markov partition in general.
