GOE statistics for Lévy matrices

  • Amol Aggarwal

    Harvard University, Cambridge, USA
  • Patrick Lopatto

    Harvard University, Cambridge, USA
  • Horng-Tzer Yau

    Harvard University, Cambridge, USA
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We establish eigenvector delocalization and bulk universality for Lévy matrices, which are real, symmetric, random matrices whose upper triangular entries are independent, identically distributed -stable laws. First, if and is bounded away from 0, we show that every eigenvector of corresponding to an eigenvalue near is completely delocalized and that the local spectral statistics of around converge to those of the Gaussian Orthogonal Ensemble as tends to . Second, we show for almost all , there exists a constant such that the same statements hold if .

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Amol Aggarwal, Patrick Lopatto, Horng-Tzer Yau, GOE statistics for Lévy matrices. J. Eur. Math. Soc. 23 (2021), no. 11, pp. 3707–3800

DOI 10.4171/JEMS/1089