Probability and Mathematical Physics Seminar

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Large Deviations of the Riemann Zeta Function and Random Walks

Speaker: Louis-Pierre Arguin, CUNY & University of Oxford

Location: Warren Weaver Hall 1302

Date: Friday, March 27, 2026, 11:10 a.m.

Synopsis:

 

In this talk, I will present a proof that the measures of level sets of the Riemann zeta function have Gaussian tail, up to a constant C, for values in suitable regimes, conditionally on the Riemann Hypothesis. As a corollary, we recover the best-known bounds on the moments on the critical line. The proof relies on the recursive scheme of prior work with Bourgade & Radziwill that is inspired by a random walk heuristic. It also combines ideas of Soundararajan and Harper. We will discuss possible improvements to the constant C as well as the connections with the Keating-Snaith Conjecture from Random Matrix Theory for the optimal constant.

 

This is joint work with Emma Bailey & Asher Roberts and Nathan Creighton.