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SUMMARY:Freezing Transition\, Characteristic Polynomials of Random Matrice
 s\, and the Riemann Zeta-Function - Keating\, J (University of Bristol)
DTSTART:20120918T105000Z
DTEND:20120918T113000Z
UID:TALK39845@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We argue that the freezing transition scenario\, previously ex
 plored in the statistical mechanics of 1/f-noise random energy models\, al
 so determines the value distribution of the maximum of the modulus of the 
 characteristic polynomials of large N x N random unitary (CUE) matrices. W
 e postulate that our results extend to the extreme values taken by the Rie
 mann 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 suppo
 rt. Our main purpose is to draw attention to possible connections between 
 the statistical mechanics of random energy landscapes\, random matrix theo
 ry\, and the theory of the Riemann zeta function.\n
LOCATION:Seminar Room 1\, Newton Institute
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