  Let $E_{n}$ be an holomorphic bundle of rank two on an algebraic curve $X$
(the degree of $E_{n}$ is $n$ apart from an additive constant). Note by
$Met(E_{n})$ the space of hermitian metrics $h$ on $E_{n}$. Also, consider
$Met(W_{n})$, the space of metrics on $H^{0}(X,E_{n})$. Although $Met(W_{n})$
is finite dimensional, it's dimension grows with $n$. So we can ask how to
obtain a way to describe particular metrics of $Met(E_{n})$ using $Met(W_{n})$.
First, we link these two spaces by two morphisms $L_{n}$ and $I_{n}$. Donaldson
gave a criterion for detecting Einstein Hermitian metrics on $Met(E_{n})$,
using a functional $\mathcal M$. We construct another functional on
$Met(W_{n})$, $\mathcal KN_{n}$, using an algebraic idea of Kempf and Ness. In
our investigations we prove that the variation of the analytic torsion, when
$h$ varies, becomes small when $n$ grows . However our main result is that
$\mathcal M-\mathcal KN\circ L_{n}$ becomes small when $n$ grows.
  Moreover, with some hypotheses, we show that Yang-Mills minimum can be
characterized(appromimately) by $\mathcal KN_{n}$. The proof of our main
theorem is based on constructing "concentrated" sections of $E_{n}$, in a way
similar to Donaldson's recent work on symplectic varieties.
