| Résume | We study the asymptotic distribution of the Fubini-Study currents associated to a sequence of singular Hermitian holomorphic line bundles on a compact normal Kähler complex space. This is a generalization of our earlier results, by allowing the base space to be singular, and by considering sequences of line bundles instead of the sequence of powers of a fixed line bundle. We also prove a universality result in the above setting, which shows that, under mild moment assumptions, the symptotic distribution of zeros of random holomorphic sections is independent of the choice of probability measure on the space of holomorphic sections. We give several applications of this result, in particular to the distribution of zeros of random polynomials. |
