  We establish, for a generically big Hermitian line bundle, the convergence of
truncated Harder-Narasimhan polygons and the uniform continuity of the limit.
As applications, we prove a conjecture of Moriwaki asserting that the
arithmetic volume function is actually a limit instead of a sup-limit, and we
show how to compute the asymptotic polygon of a Hermitian line bundle, by using
the arithmetic volume function.
