  In this note we employ methods borrowed from spin glass theory to study the
phase space structure of fields in an inflating universe. In particular, we
compute the overlap distribution of a suitably coarse-grained, massless scalar
on a 1+1 dimensional (hence baby) de Sitter background, and find that (after an
appropriate shift and rescaling) it is given by a Gumbel distribution. We also
calculate the triple overlap distribution of this system, whose characteristic
function turns out to be a product of two Gumbel factors.
