---
_id: '9230'
abstract:
- lang: eng
  text: "We consider a model of the Riemann zeta function on the critical axis and
    study its maximum over intervals of length (log T)θ, where θ is either fixed or
    tends to zero at a suitable rate.\r\nIt is shown that the deterministic level
    of the maximum interpolates smoothly between the ones\r\nof log-correlated variables
    and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to
    1/4’ in the second order. This provides a natural context where extreme value
    statistics of\r\nlog-correlated variables with time-dependent variance and rate
    occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate
    for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian
    correction. This correction is expected to be present for the\r\nRiemann zeta
    function and pertains to the question of the correct order of the maximum of\r\nthe
    zeta function in large intervals."
acknowledgement: The research of L.-P. A. is supported in part by the grant NSF CAREER
  DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon
  2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
  No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft
  (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID
  443891315 within SPP 2265 and Project-ID 446173099.
article_number: '2103.04817'
article_processing_charge: No
arxiv: 1
author:
- first_name: Louis-Pierre
  full_name: Arguin, Louis-Pierre
  last_name: Arguin
- first_name: Guillaume
  full_name: Dubach, Guillaume
  id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
  last_name: Dubach
  orcid: 0000-0001-6892-8137
- first_name: Lisa
  full_name: Hartung, Lisa
  last_name: Hartung
citation:
  ama: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
    function over intervals of varying length. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2103.04817">10.48550/arXiv.2103.04817</a>
  apa: Arguin, L.-P., Dubach, G., &#38; Hartung, L. (n.d.). Maxima of a random model
    of the Riemann zeta function over intervals of varying length. <i>arXiv</i>. <a
    href="https://doi.org/10.48550/arXiv.2103.04817">https://doi.org/10.48550/arXiv.2103.04817</a>
  chicago: Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a
    Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>,
    n.d. <a href="https://doi.org/10.48550/arXiv.2103.04817">https://doi.org/10.48550/arXiv.2103.04817</a>.
  ieee: L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the
    Riemann zeta function over intervals of varying length,” <i>arXiv</i>. .
  ista: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
    function over intervals of varying length. arXiv, 2103.04817.
  mla: Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta
    Function over Intervals of Varying Length.” <i>ArXiv</i>, 2103.04817, doi:<a href="https://doi.org/10.48550/arXiv.2103.04817">10.48550/arXiv.2103.04817</a>.
  short: L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).
date_created: 2021-03-09T11:08:15Z
date_published: 2021-03-08T00:00:00Z
date_updated: 2025-04-14T07:43:51Z
day: '08'
department:
- _id: LaEr
doi: 10.48550/arXiv.2103.04817
ec_funded: 1
external_id:
  arxiv:
  - '2103.04817'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2103.04817
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
status: public
title: Maxima of a random model of the Riemann zeta function over intervals of varying
  length
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...