Correlation Functions for β=1 Ensembles of Matrices of Odd Size
Using the method of Tracy and Widom we rederive the correlation functions for β=1 Hermitian and real asymmetric ensembles of N x N matrices with N odd.
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arXiv subjects
Christopher D Sinclair
Publications and source records attributed to Christopher D Sinclair.
The Ginibre ensemble of real random matrices and its scaling limits
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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