Statistical Static Timing Analysis of VLSI as the Statistics of Correlated Extremes

In this study, a path-based Statistical Static Timing Analysis (SSTA) is formulated as a problem within the statistics of correlated extremes. For extreme value statistics with correlations, a novel approach to studying such systems, when the correlations are small, is developed. The approach considers a system from the first principals, starting from the multivariable characteristic function. Analytical solutions to the problem of weakly correlated extremes are obtained in the form of corrections to the Gumbel distribution. These solutions are compared with Monte Carlo simulations. The applicability limits of the proposed solutions are studied. An algorithm to estimate the covariance matrix of a timing graph is proposed.