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Under the assumption that elements have power law decaying tails, we prove a strong law of large numbers for $\\log \\perm A$. We calculate the values of the limit $\\lim_{n \\to \\infty}\\frac{\\log \\perm A}{n \\log n}$ in terms of the exponent of the power law distribution decay, and observe a first order phase transition in the limit as the mean becomes infinite. 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