Résume | I would like to explain the large deviation estimates for zeros of random holomorphic sections on;punctured Riemann surfaces. These estimates are then employed to yield estimates for the respective hole probabilities. A particular case covered by our setting is that of cusp forms on arithmetic surfaces. Most of the results we obtain allow for reasonably general probability distributions on holomorphic sections, which shows the universality of these estimates. We also extend these results to the case of certain higher dimensional complete Hermitian manifolds, which are not necessarily assumed to be compact. |