April 26, 2012. Yan V. Fyodorov (Queen Mary, University of London). Freezing Transition: from 1/f landscapes to Characteristic Polynomials of Random Matrices and the Riemann zeta-function.
In the talk (based on a joint work with G.Hiary and J.Keating; arXiv:1202.4713) I will argue that the freezing transition scenario, previously conjectured to take place in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials of large random unitary (CUE) matrices. I then conjecture that the results extend to the large values taken by the Riemann zeta-function over stretches of the critical line s=1/2+it of constant length, and present the results of numerical computations of the large values of ζ(1/2+it). The 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 function.
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List of talks at previous sessions of the seminar. |