  We establish a connection between the cascading of gluon momenta modeled with
the diffusive approximation of the Balitsky-Fadin-Kuraev-Lipatov kernel and the
thermodynamics of directed polymers on a tree with disorder. Using known
results on the low-temperature spin-glass phase of this statistical-mechanic
problem we describe the dynamical phase space of gluon transverse momenta near
saturation including its fluctuation pattern. It exhibits a nontrivial
clustering structure, analoguous to ``hot spots'', whose distributions are
derived and possess universal features in common with other spin-glass systems.
