The Ginibre ensemble of real random matrices and its scaling limits

Details The Ginibre ensemble of real random matrices and its scaling limits The Ginibre ensemble of real random matrices and its scaling limits

2008-05-20

arxiv.org/abs/0805.2986v1

Physics

Mathematical Physics

47 pages, 8 figures

Scientific paper

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

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