Christopher Atherfold

A model problem for the distribution of sums random multiplicative functions

In seminal work of Diaconis and Shahshahani, they were able to prove a convergence in distribution result on the logarithm of the characteristic polynomial for unitary NxN matrices. It turns out this can be viewed as a simpler model for complete sums of Steinhaus random multiplicative functions. In this talk, I will discuss recent work of Joseph Najnudel and myself where we determined the distribution of the secular coefficients in the critical case, as well as the recent remarkable work of Gorodetsky—Wong on the Steinhaus sum. Both of these are related to the phenomenon of better than squareroot cancellation and Gaussian multiplicative chaos, which I will try to motivate in this talk. If I have time, I will also relate these to upcoming work on the Riemann zeta function.