RANDOM MATRICES WITH SLOW CORRELATION DECAY
Keyword(s):
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.
2019 ◽
Vol 22
(04)
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pp. 1950024
2018 ◽
Vol 173
(1-2)
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pp. 293-373
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2016 ◽
Vol 05
(02)
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pp. 1650006
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2013 ◽
Vol 02
(01)
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pp. 1250015
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2016 ◽
Vol 2016
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pp. 1-12
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2019 ◽
Vol 27
(2)
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pp. 89-105
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