Random multiplicative functions have received a lot of attention in
recent years as a model for the Riemann zeta function
on short intervals on the critical line. By now, we have a good
understanding of their moments and a decent idea of their
extremal behaviour, i.e., almost sure upper and lower bounds, due
to work of Harper, Lau-Tenenbaum-Wu and others.
More recently, Soundararajan and Zaman introduced a new model that
can be thought of as a simplified function field
analogue of random multiplicative functions, and they proved moments
bounds for these quantities akin to those of
Harper. In this talk, I will discuss almost sure lower bounds for this
quantity and some of the simplifications that can
be made in the proof when compared to the random multiplicative setting.