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

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 ζ(s) over sections of the critical line s=1/2+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.

• Publication year

  2012

• Venue

  Physical Review Letters

• Publication date

  2012-02-21

• Fields of study

  Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1103/PhysRevLett.108.170601arXiv 1202.4713PMID 22680847
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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