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We propose a scheme for maintaining the requested SIR of each user under uncertainty of system parameters in the power control of interference limited wireless networks. In doing so, we keep the outage probability of users below their predefined threshold with minimal power consumption. To reduce the complexity, we apply the notion of chance constraint robust optimization to the outage probability. This approach preserves the convexity of the problem and maintains its tractability. For solving the reformulated problem, a distributed probabilistic robust power algorithm is developed based on the standard interference function and local convergence, which utilizes infrequent message passing. We derive the conditions for the convergence of our algorithm, and prove the optimality of the equilibrium.