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As the technology scales into 90 nm and below, process-induced variations become more pronounced. In this paper, we propose an efficient stochastic method for analyzing the voltage drop variations of on-chip power grid networks, considering log-normal leakage current variations with spatial correlation. The new analysis is based on the Hermite polynomial chaos (PC) representation of random processes. Different from the existing Hermite PC based method for power grid analysis, which models all the random variations as Gaussian processes without considering spatial correlation. The new method focuses on the impacts of stochastic sub-threshold leakage currents, which are modeled as log-normal distribution random variables, on the power grid voltage variations. To consider the spatial correlation, we apply orthogonal decomposition to map the correlated random variables into independent variables. Our experiment results show that the new method is more accurate than the Gaussian-only Hermite PC method using the Taylor expansion method for analyzing leakage current variations, and two orders of magnitude faster than the Monte Carlo method with small variance errors. We also show that the spatial correlation may lead to large errors if not being considered in the statistical analysis.