O. Safronov and B. Vainberg Eigenvalue estimates for random Schr\"odinger operators (157K, pdf) ABSTRACT. In this paper we study the negative eigenvalues $\lambda_j$ of the Schr\"odinger operator $-\Delta-V(x)$. We prove that $\sum_j|\lambda_j|^\gamma$ converges for random $L^{d+2\gamma}$-potentials with probability 1. One of the important assumptions in our paper is that the expectation of $V(x)$ is zero at every point $x$.