Add to ORKGWe consider the extremes of the logarithm of the characteristic polynomial of matrices from the C$\beta$E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) towards the sum of a Gumbel variable and another independent variable, which we characterize as the total mass of a "derivative martingale". We also provide a description of the landscape near extrema points.Comment: Appendix B is an adaptation of estimates from arXiv:1607.00243 and uses their source file as template. V2 corrects a mistake in Section 9, Lemma 9.
Let $g$ be a random matrix distributed according to uniform probability measure on the finite genera...
Motivated by recently discovered relations between logarithmically correlated Gaussian processes and...
to appear in Proceedings of the AMSGiven a sequence of complex numbers ρ_n, we study the asymptotic ...
Let $\Gamma \subset \mathbb C$ be a curve of class $C(2,\alpha)$. For $z_{0}$ in the unbounded compo...
18 pages, 5 figures. Typos corrected and some additional discussion added18 pages, 5 figures. Typos ...
Continuation of Fyodorov--Keating conjectures, connections with random multiplicative functions
For arbitrary β > 0, we use the orthogonal polynomials techniques developed in (Killip and Nenciu in...
We prove the Central Limit Theorem (CLT) for the number of eigenvalues near the spectrum edge for ce...
We will prove the Berry-Esseen theorem for the number counting function of the circular $\beta$-ense...
The problem of calculating the scaled limit of the joint moments of the characteristic polynomial, a...
AbstractLet {Xn;n⩾1} be a strictly stationary sequence of positively associated random variables wit...
The article begins with a quantitative version of the martingale central limit theorem, in terms of ...
Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M compl...
Author's draft, December 21, 2007We consider the Breitung (2002, Journal of Econometrics 108, 343–36...
A recent paper (Jokela et al 2008 Preprint arXiv:0806.1491) contains a surmise about an expectation ...
Let $g$ be a random matrix distributed according to uniform probability measure on the finite genera...
Motivated by recently discovered relations between logarithmically correlated Gaussian processes and...
to appear in Proceedings of the AMSGiven a sequence of complex numbers ρ_n, we study the asymptotic ...
Let $\Gamma \subset \mathbb C$ be a curve of class $C(2,\alpha)$. For $z_{0}$ in the unbounded compo...
18 pages, 5 figures. Typos corrected and some additional discussion added18 pages, 5 figures. Typos ...
Continuation of Fyodorov--Keating conjectures, connections with random multiplicative functions
For arbitrary β > 0, we use the orthogonal polynomials techniques developed in (Killip and Nenciu in...
We prove the Central Limit Theorem (CLT) for the number of eigenvalues near the spectrum edge for ce...
We will prove the Berry-Esseen theorem for the number counting function of the circular $\beta$-ense...
The problem of calculating the scaled limit of the joint moments of the characteristic polynomial, a...
AbstractLet {Xn;n⩾1} be a strictly stationary sequence of positively associated random variables wit...
The article begins with a quantitative version of the martingale central limit theorem, in terms of ...
Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M compl...
Author's draft, December 21, 2007We consider the Breitung (2002, Journal of Econometrics 108, 343–36...
A recent paper (Jokela et al 2008 Preprint arXiv:0806.1491) contains a surmise about an expectation ...
Let $g$ be a random matrix distributed according to uniform probability measure on the finite genera...
Motivated by recently discovered relations between logarithmically correlated Gaussian processes and...
to appear in Proceedings of the AMSGiven a sequence of complex numbers ρ_n, we study the asymptotic ...