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Random Matrix Theory and ζ(1/2+it)
Abstract: We study the characteristic polynomials Z(U, θ) of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the
Random Matrix Theory and L-Functions at s= 1/2
Abstract: Recent results of Katz and Sarnak [8, 9] suggest that the low-lying zeros of families of L-functions display the statistics of the eigenvalues of one of the compact groups of matrices U(N),
Integral moments of L-functions
We give a new heuristic for all of the main terms in the integral moments of various families of primitive $L$-functions. The results agree with previous conjectures for the leading order terms. Our
The Riemann Zeros and Eigenvalue Asymptotics
It is speculated that the Riemann dynamics is related to the trajectories generated by the classical hamiltonian Hcl=XP, and very refined features of the statistics of the tn can be computed accurately from formulae with quantum analogues.
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
H = xp and the Riemann Zeros
The Riemann hypothesis 1,2 states that the complex zeros of ζ(s) lie on the critical line Re s=1/2; that is, the nonimaginary solutions E n of (1) are all real. Here we will present some evidence
The evolution of bubble size distributions in volcanic eruptions
We review observations of bubble size distributions (BSDs) generated during explosive volcanic eruptions and laboratory explosions, as inferred from vesicle size distributions found in the end
Freezing transitions and extreme values: random matrix theory, and disordered landscapes
  • Y. Fyodorov, J. Keating
  • Physics, Medicine
    Philosophical Transactions of the Royal Society A…
  • 26 November 2012
We argue that the freezing transition scenario, previously conjectured to occur in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution
The variance of the number of prime polynomials in short intervals and in residue classes
We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial
Inferring volcanic degassing processes from vesicle size distributions
Both power law and exponential vesicle size distributions (VSDs) have been observed in many different types of volcanic rocks. We present results of computer simulations and laboratory analogue