2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/195974We 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.12 pages, 4 figures; revised version with modified title, some clarifications, and corrections of misprints; Fig.4 updated, results unchangedHigh Energy Physics - PhenomenologyStatistical MechanicsHigh Energy Physics - Theorytext