Recent research shows the ubiquity of random walk models in problems in analytic number theory as well as Gaussian multiplicative chaos and log-correlations. This comes into the distribution of ζ-values on the 1/2-line, sums of multiplicative functions (particularly divisor functions), and even the solution to various Diophantine problems, and shows direct links and inspiration from Quantum chaos theory. Adam Harper will give his three Aisenstadt lectures at the meeting.