Spectral fluctuations for the multi-dimensional Anderson model

  • Yoel Grinshpon

    The Hebrew University of Jerusalem, Israel
  • Moshe J. White

    The Hebrew University of Jerusalem, Israel
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Abstract

In this paper, we examine fluctuations of polynomial linear statistics for the Anderson model on for any potential with finite moments. We prove that if normalized by the square root of the size of the truncated operator, these fluctuations converge to a Gaussian limit. For a vast majority of potentials and polynomials, we show that the variance of the limiting distribution is strictly positive, and we classify in full the rare cases in which this does not happen.

Cite this article

Yoel Grinshpon, Moshe J. White, Spectral fluctuations for the multi-dimensional Anderson model. J. Spectr. Theory 12 (2022), no. 2, pp. 591–615

DOI 10.4171/JST/412