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Let (X _jk ) _j,k ≥ 1 be i.i.d. complex random variables such that |X _jk | is in the domain of attraction of an α-stable law, with 0 < α < 2. Our main result is a heavy tailed counterpart of Girko’s circular law. Namely, under some additional smoothness assumptions on the law of X _jk , we prove that there exist a deterministic sequence a _n ~ n ^1/α and a probability measure μ _α on depending only on α such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix converges weakly to μ _α as n → ∞. Our approach combines Aldous & Steele’s objective method with Girko’s Hermitization using logarithmic potentials. The underlying …