Maxima of a random model of the Riemann zeta function over intervals of varying length
Arguin, Louis-Pierre
Dubach, Guillaume
Hartung, Lisa
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.
It is shown that the deterministic level of the maximum interpolates smoothly between the ones
of log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from
3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of
log-correlated variables with time-dependent variance and rate occur. A key ingredient of the
proof is a precise upper tail tightness estimate for the maximum of the model on intervals of
size one, that includes a Gaussian correction. This correction is expected to be present for the
Riemann zeta function and pertains to the question of the correct order of the maximum of
the zeta function in large intervals.
2021
info:eu-repo/semantics/preprint
doc-type:preprint
text
http://purl.org/coar/resource_type/c_816b
https://research-explorer.ista.ac.at/record/9230
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>
eng
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2103.04817
info:eu-repo/semantics/altIdentifier/arxiv/2103.04817
info:eu-repo/grantAgreement/EC/H2020/754411
info:eu-repo/semantics/openAccess