Wednesday, February 22, 2012

1202.4713 (Yan V. Fyodorov et al.)

Freezing Transition, Characteristic Polynomials of Random Matrices, and
the Riemann Zeta-Function

Yan V. Fyodorov, Ghaith A Hiary, Jonathan P. Keating
We argue that the freezing transition scenario, previously explored in the
statistical mechanics of 1/f-noise random energy models, also determines the
value distribution of the maximum of the modulus of the characteristic
polynomials of large N x N random unitary (CUE) matrices. We postulate that our
results extend to the extreme values taken by the Riemann zeta-function zeta(s)
over sections of the critical line s=1/2+it of constant length and present the
results of numerical computations in support. Our main purpose is to draw
attention to possible connections between the statistical mechanics of random
energy landscapes, random matrix theory, and the theory of the Riemann zeta
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