David Belius

Maximum of the Characteristic Polynomial of Random Unitary Matrices

It was recently conjectured by Fyodorov, Hiary and Keating that the maximum of the characteristic polynomial on the unit circle of a

COVER LEVELS AND RANDOM INTERLACEMENTS

{N\times N}

Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line

N×N random unitary matrix sampled from the Haar measure grows like

The TAP-Plefka variational principle for the spherical SK model

{CN/({\rm log} N)^{3/4}}

Maximum of the Ginzburg-Landau fields

CN/(logN)3/4 for some random variable C. In this paper, we verify the leading order of this conjecture, that is, we prove that with high probability the maximum lies in the range