Resolving a question of Lévy, Wintner started the study of a Rademacher random multiplicative
function in the 40's.
This is a genuine multiplicative function supported on the squarefree
integers such that its values at primes are given
by ± 1 independent random variables. Several results concerning upper and omega bounds, low and high moments
and central limit theorems have been proved. In this talk I will discuss sign changes of the partial sums of
two models
of random multiplicative functions: the Rademacher case and the completely multiplicative random case. I will also
discuss the results in the literature about sign changes of the partial sums of the deterministic counterparts
such as the
Liouville and the Möbius function.