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In this paper we study the limiting distribution of the $k$ smallest gapsbetween eigenvalues of three kinds of random matrices -- the Ginibre ensemble,the Wishart ensemble and the universal unitary ensemble. All of them follow aPoissonian ansatz. More precisely, for the Ginibre ensemble we have a globalresult in which the $k$-th smallest gap has typical length $n^{-3/4}$ withdensity $x^{4k-1}e^{-x^4}$ after normalization. For the Wishart and theuniversal unitary ensemble, it has typical length $n^{-4/3}$ and has density$x^{3k-1}e^{-x^3}$ after normalization.

Smallest Gaps Between Eigenvalues of Random Matrices With Complex Ginibre, Wishart and Universal Unitary Ensembles