2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/29899We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We also map this system to a model of population dynamics with fixed total population. Our previous results translate to static and expanding population clusters, depending on the birth and death rates. A novel ``pseudo-travelling wave'' is observed in some sectors of parameter space.4 pages, 2 figures, submitted to Physical Review LettersStatistical MechanicsQuantitative Biologytext