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The noise in the circular law and the Gaussian free field. (English) Zbl 1130.60030
The authors prove a general central limit theorem for the eigenvalues of random matrices with Gaussian entries, and apply their findings to the planar Gaussian free field.

MSC:
60F05 Central limit and other weak theorems
15B52 Random matrices (algebraic aspects)
15A18 Eigenvalues, singular values, and eigenvectors
60K40 Other physical applications of random processes
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