Seminar on Disorder and strong electron correlations: "Freezing transition: From 1/f landscapes to characteristic polynomials of random matrices and the Riemann zeta-function"
Starts 24 May 2012 12:30
Ends 24 May 2012 20:00
Central European Time
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
I will argue that the freezing transition scenario, previously conjectured to take place in Statistical Mechanics of 1/f-type Random Energy Model, 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 \zeta(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.
The presentation will be based on the joint work with G.Hiary and J.P. Keating: Phys. Rev. Lett. 108 , 170601 (2012)