Abstract: Tower of coverings has been studied extensively in Riemannian geometry case. In this talk, I will focus on a tower of coverings over a compact Kahler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, I will show that the tower is Bergman stable with effective estimates, which imply the equidistribution for random zero currents of holomorphic sections. Moreover, I am also going to talk about a variance estimate of the random zero currents, which yields the almost sure convergence under certain geometric conditions. This is a joint work with Yuan Yuan.