Freezing transition, characteristic polynomials of random matrices, and the Riemann zeta-function

YV Fyodorov, Ghaith Hiary, Jon P Keating

Research output: Contribution to journalArticle (Academic Journal)peer-review

58 Citations (Scopus)

Abstract

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 ! N random unitary matrices. We postulate that our results extend to the extreme values taken by the Riemann zeta function !ðsÞ over sections of the critical line s ¼ 1=2 þ 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 function.
Original languageEnglish
Article number170601
JournalPhysical Review Letters
Volume108
Issue number17
DOIs
Publication statusPublished - 26 Apr 2012

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