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We give a closed form for the correlation functions of ensembles of a classof asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrixformed from a $2 \times 2$ matrix kernel associated to the ensemble. We applythis result to the real Ginibre ensemble and compute the bulk and edge scalinglimits of its correlation functions as the size of the matrices becomes large.

The Ginibre ensemble of real random matrices and its scaling limits