  The irreducible decomposition of successive restriction and induction of
irreducible representations of a symmetric group gives rise to a Markov chain
on Young diagrams keeping the Plancherel measure invariant. Starting from this
Res-Ind chain, we introduce a not necessarily Markovian continuous time random
walk on Young diagrams by considering a general pausing time distribution
between jumps according to the transition probability of the Res-Ind chain. We
show that, under appropriate assumptions for the pausing time distribution, a
diffusive scaling limit brings us concentration at a certain limit shape
depending on macroscopic time which leads to a similar consequence to the
exponentially distributed case studied in our earlier work. The time evolution
of the limit shape is well described by using free probability theory. On the
other hand, we illustrate an anomalous phenomenon observed with a pausing time
obeying a one-sided stable distribution, heavy-tailed without the mean, in
which a nontrivial behavior appears under a non-diffusive regime of the scaling
limit.
