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Freezing transition for the Riemann zeta function on a short interval

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Louis-Pierre Arguin
CUNY Stony Brook
Wed, 13/06/2018 - 16:15 - 17:15
MPIM Lecture Hall

In this talk, we will present a proof of the freezing transition for the Riemann zeta function as conjectured by Fyodorov, Hiary & Keating. The connection with log-correlated fields will be emphasized. The problem is related to understanding moments of zeta on a typical short interval. The proof relies on techniques developed to understand the leading order of the maximum of zeta. If time permits, we will discuss the “one-step replica symmetry breaking behaviour” (1-RSB) which can be proved for a simplified model of zeta.

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