On equidistribution theorem for multi-sequences of holomorphic line bundles

Given several sequences of Hermitian holomorphic line bundles $\{(L_{kp},h_{kp}){\}}_{p=1}^{\mathrm{\infty }}$, we establish the distribution of common zeros of random holomorphic sections of $L_{kp}$ with respect to singular measures. We also study the dimension growth for a sequence of pseudo-effective line bundles.