Hybrid Statistics of the Maxima of a Random Model of the Zeta Function over Short Intervals

Christine K. Chang

We will present a matching upper and lower bound for the right tail probability of the maximum of a random model of the Riemann zeta function over short intervals. In particular, we show that the right tail interpolates between that of log-correlated and IID random variables as the interval varies in length. We will also discuss a new normalization for the moments over short intervals. This result follows the recent work of Arguin-Dubach-Hartung and is inspired by a conjecture by Fyodorov-Hiary-Keating on the local maximum over short intervals.

https://mathtube.org/lecture/video/hybrid-statistics-maxima-random-model-zeta-function-over-short-intervals