The maximum of the CUE field
By Elliot Paquette, Ofer Zeitouni. 2016
95 citations recorded by the source corpus.
Let $U_N$ denote a Haar Unitary matrix of dimension N, and consider the field \[ {\bf U}(z) = \log |\det(1-zU_N)| \] for z in the unit disk. Then, \[ \frac{\max_{|z|=1} {\bf U}(z) -\log N + \frac{3}{4} \log\log N} {\log\log N} \to 0 \] in probability. This provides a verification up to second order of a conjecture of Fyodorov, Hiary and Keating, improving on the recent first order verification of Arguin, Belius and Bourgade.
Subfields: Algebra and Number Theory, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/84b39a02db3f8127491c799e91851b480b54813a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Joseph Najnudel
- L. Arguin
- P. Bourgade
- Maksym Radziwill
- David Belius
- Christian Webb
- Eero Saksman
- Kannan Soundararajan
In Mathematical Physics
- Joseph Najnudel
- L. Arguin
- Christian Webb
- Eero Saksman
- P. Bourgade
- Maksym Radziwill
- Kannan Soundararajan
- David Belius
In Statistics and Probability
- Joseph Najnudel
- L. Arguin
- P. Bourgade
- Kannan Soundararajan
- Christian Webb
- David Belius
- Eero Saksman
- Jasper A. Vrugt
Citations in the corpus
- On the extreme values of the Riemann zeta function on random intervals of the critical line (2016, methodology): “This conjecture is not fully proven, but Chhaibi, Madaule and Najnudel in [13] have recently shown that the family (1.2) of random variables is tight, improving successive results by Arguin, Belius and Bourgade [3] and by Paquette and Zeitouni [26].”
- The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line (2016, background): “[3, 68] (see also [2, 70, 22] for related results in the setting of random matrices).”
- Extreme value statistics of correlated random variables: A pedagogical review (2019, unknown): “[249] E.”
- Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line (2016, methodology): “The identification of an approximate branching random walk structure within the sum ∑ p≤X p −s was used in [3] to study the extrema of a random model of the zeta function, and in the subsequent works regarding the large values of characteristic polynomials [2,12,26,33] and of the zeta function [32].”