Thursday 24th May seminar

[Cond.Matt. & Stat.Mech.Section]

SEMINAR on   Disorder and strong electron correlations

 

Thursday, 24 May -  11:30 a.m.

 

Luigi Stasi Seminar Room,  Leonardo Building - first floor

 

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"



Abstract

 

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)