Title: On the distribution of sums of random multiplicative functions


Abstract: A random multiplicative function is a multiplicative function α(n) defined on the positive integers, such that its values on primes, (α(p)), (p=2,3,5,...), are i.i.d. random variables. Such functions were introduced in the 40s by Wintner to model deterministic arithmetic functions, such as the famous Möbius function.
A basic question in the field is finding the limiting distribution of the sum of α(n) from n=1 up to n=x, possibly restricted to a subset of integers of interest. Again, the motivation is to gain insight into sums of deterministic functions which are currently poorly understood.
In the talk I will explain and motivate this basic question, and survey the state of the art on it and the methods involved. I will also describe recent work, joint work with Mo Dick Wong, where we are able to find the limiting distribution in many new instances of interest. The distribution we find is non-Gaussian, in contrast to all previous works.


Livestream/Recording: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=d69f56a3-9187-40ba-b5af-b26d0067dd43