We study the maximum of a random model for the Riemann zeta function (on the critical line at height $T$) on the interval $[-(\log T)^{\theta}, (\log T)^{\theta})$, where $\theta = (\log \log T)^{-a}$, 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 $\theta$. 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.
Régis de la Bretèche
