On the Characteristic Polynomial¶ of a Random Unitary Matrix

By C. Hughes, Jon P Keating, Neil O'Connell. 2001

235 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d758fc73bab53354266d176c0b4585c9a6ef044f

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Fluctuations of eigenvalues and second order Poincaré inequalities (2007, background): “[30], Soshnikov [48], Israelson [31] and Wieand [52].”
Random Matrix Theory and ζ(1/2+it) (2000, background): “If N is large, this is asymptotic to [19]”
Moderate Deviations via Cumulants (2010, background): “.5] the asymptotic behaviour of ℜlog(Z) an √ logn for scaling ranges an = √ lognand √ logn ≪ an ≪ n/ √ lognis considered. The circular orthogonal and circular symplectic ensembles were not studied in [18]. Proof of Theorem 4.1. In[23, eq. (47)]anintegralrepresentation ofthecumulants ofℜlog(Z) for th”
The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line (2016, background): “n the global scale. On the global scale, it is known that the logarithm of the characteristic polynomial of a Haar distributed random matrix behaves asymptotically like a log-correlated Gaussian ﬁeld [40]. In [75] it was shown that after an appropriate normalization, as the size of the matrix tends ”
Eigenvalue distributions of random unitary matrices (2002, background): “Also closely related are the results of Keating and Snaith [20] for the characteristic polynomial of a random unitary matrix and the paper by Hughes, Keating, and O’Connell [15]; in particular [ 15 ] provides an explanation of the unusual covariance (3).”
Maxima of a randomized Riemann zeta function, and branching random walks (2015, background): “comparison inequality that requires control of logTpoints. Fyodorov, Hiary and Keating motivated Conjecture 1 in [14, 15] using a connection to random matrices. There is convincing evidence, see e.g. [20, 21], that the values of the zeta function in an interval of the critical line are well modelled”
Gaussian fluctuations for non-Hermitian random matrix ensembles (2005, background): “While certain techniques may be imported from the Hermitian setting, these ensembles have their own structure and their analysis requires a separate set of tools; see, for example, [8, 18, 21, 22] and [30].”