Emma Bailey

City University of New York City University of New York

Large deviations of random matrix and number theoretic central limit theorems

Mathematical Physics Seminar

4th November 2022, 1:45 pm – 3:30 pm
Fry Building, 2.04

Central limit theorems inform us about the typical size of a random variable. For example, we know that for a random unitary matrix $U$, its characteristic polynomial is typically of size roughly $\exp(\sqrt{ 1/2 \log N} )$ thanks to the central limit theorem of Keating and Snaith. One might be interested in atypical behaviour, for example what is the likelihood of the characteristic polynomial being abnormally large? This would in turn provide a conjecture for the probability of large values of the Riemann zeta function. Joint with Louis-Pierre Arguin we prove (presumably) sharp upper bounds for large deviations of zeta which match the corresponding known random matrix result. The talk will assume no number theoretic knowledge (though local experts are welcome!).


Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/b80dc304a8314b58a52736d7be6862f31d

Organiser: Thomas Bothner

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