Seminar

# Large fluctuations of random multiplicative functions

#### Adam Harper - University of Warwick

Random multiplicative functions $f(n)$ are a well studied random model for deterministic multiplicative functions like Dirichlet characters or the Mobius function. Arguably the first question ever studied about them, by Wintner in 1944, was to obtain almost sure bounds for the largest fluctuations of their partial $\sum_{n \leq x} f(n)$, seeking to emulate the classical Law of the Iterated Logarithm for independent random variables. It remains an open question to sharply determine the size of these fluctuations, and in this talk I will describe a new result in that direction. I hope to get to some interesting details of the new proof in the latter part of the talk, but most of the discussion should be widely accessible.

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Meeting ID: 921 756 188

Organizers
Pär Kurlberg
KTH Royal Institute of Technology
Lilian Matthiesen
KTH Royal Institute of Technology

# ProgramContact

Pär Kurlberg

kurlberg@math.kth.se

Lilian Matthiesen

lilian.matthiesen@math.kth.se

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