Maxima of a random model of the Riemann zeta function on longer intervals (and branching random walks)

Abstract: 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 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.

mathematical physicsprobability

Audience: researchers in the discipline

Oxford Random Matrix Theory Seminars

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