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arXiv · 2207.00674

Gaussian Fluctuation for Smoothed Local Correlations in CUE

Alexander Soshnikov
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Abstract

Motivated by the Rudnick-Sarnak theorem we study limiting distribution of smoothed local correlations of the form $$ \sum_{j_1, j_2, \ldots, j_n} f(N\*(\theta_{j_2}-\theta_{j_1}), N\*(\theta_{j_3}-\theta_{j_1}), \ldots, N\*(\theta_{j_n}-\theta_{j_1}))$$ for the Circular United Ensemble of random matrices for sufficiently smooth test functions.

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BibTeXRIS

Alexander Soshnikov. 2022-07-01. Gaussian Fluctuation for Smoothed Local Correlations in CUE. https://doi.org/10.1007/s10955-022-03028-9

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