Abstract
The multifractal nature of the probability distribution for the head of a directed polymer in a (1+1)-dimensional disordered medium is derived analytically. This is achieved by using a mapping of the model into a corresponding ``toy'' model which consists of a classical particle in a combination of a harmonic potential and a long-ranged random potential. We use the solution of the latter problem that incorporates replica-symmetry breaking within the framework of a variational approximation. The results are expressed in terms of a distribution f(\ensuremath{\alpha}) reminiscent of that used in dynamical systems. We compare our results with numerical simulations.
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