4.5 Article

Matrix regularizing effects of Gaussian perturbations

期刊

出版社

WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219199717500286

关键词

Gaussian perturbation; Wegner estimate; Minami estimate; deformed GUE; deformed GOE

资金

  1. NSF grant [PHY-1305472, DMS-0846325]
  2. ISF grant [1048/11, 861/15, 147/15]
  3. IRG grant SPTRF
  4. ERC [639305]
  5. European Research Council (ERC) [639305] Funding Source: European Research Council (ERC)

向作者/读者索取更多资源

The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for H = A + V, where A is the base matrix and V is sampled from the GOE or the GUE random matrix ensembles. We bound the mean number of eigenvalues of H in an interval, and present tail bounds for the distribution of the Frobenius and operator norms of H-1 and for the distribution of the norm of H-1 applied to a fixed vector. The bounds are uniform in A and exceed the actual suprema by no more than multiplicative constants. The probability of multiple eigenvalues in an interval is also estimated.

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