We study the maximum of a random model for the Riemann zeta function
(on the critical line at height T)
on the interval [-(log T)θ, (log T)θ),
where θ = (log log T)-a, with 0 < a < 1.
we obtain the leading order
as well as the logarithmic correction of the maximum. As it turns out, a good toy model
is a collection
of independent BRW’s, where the number of independent copies depends on θ.
In this talk I will try to
motivate our results by mainly focusing on this toy model.
The talk is based on joint work in progress with L.-P. Arguin and G. Dubach.