I would like to know if there are any theoretical results on the distribution of the eigenvalues of Hankel matrices. I seek a result like the Marchenko–Pastur distribution for random matrices.

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    $\begingroup$ This is studied in the paper by Bryc, Dembo, Jiang (Annals of probability 2006). $\endgroup$ – Igor Rivin Mar 21 '18 at 2:42

As far as I know, there are no known results regarding extremal eigenvalues.

The only concrete result I know of regarding the density of states of random Hankel matrices is the following:

(Bose and Sen, 2006) For a Hankel matrix constructed from i.i.d. standard Gaussians, the limiting density of states is a normal distribution with mean 0 and variance 2/3.

  • $\begingroup$ Thanks. Yes i have seen this article. I am looking for the min and max of the eigenvalues. $\endgroup$ – david Sep 13 '12 at 7:59
  • $\begingroup$ That's as much as I know... good luck hunting! $\endgroup$ – Jiahao Chen Sep 13 '12 at 13:17

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