ANOMALOUS FLUCTUATIONS OF DIRECTED POLYMERS IN RANDOM-MEDIA

A systematic analysis of large-scale fluctuations in the low-temperatu re pinned phase of a directed polymer in a random potential is describ ed. These fluctuations come from rare regions with nearly degenerate ' 'ground states.'' The probability distribution of their sizes is found to have a power-law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the map ping to the noisy Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet ex citations and a recent variational approach with ''broken replica symm etry.'' It is argued that the power-law distribution of large thermall y active excitations is a consequence of the continuous statistical '' tilt'' symmetry of the directed polymer, the breaking of which gives r ise to the large active excitations in a manner analogous to the appea rance of Goldstone modes in pure systems with a broken continuous symm etry.