  In this paper, we study large $c$ Virasoro blocks by using the Zamolodchikov
monodromy method beyond its known limits. We give an analytic proof of our
recent conjectur, which implied that the asymptotics of the large $c$ conformal
blocks can be expressed in very simple forms, even if outside its known limits,
namely the semiclassical limit or the heavy-light limit. In particular, we
analytically discuss the fact that the asymptotic behavior of large $c$
conformal blocks drastically changes when the dimensions of external primary
states reach the value $\frac{c}{32}$, which is conjectured by our numerical
studies. The results presented in this work imply that the general solutions to
the Zamolodchikov recursion relation are given by Cardy-like formula, which is
an important conclusion that can be numerically drawn from our recent works.
Mathematical derivations and analytical results imply that, in the bulk, the
collision behavior between two heavy particles may undergo a remarkable
transition associated with their masses.
