Abstract
We study a model of polymers with random charges; the possible shapes of the polymer are represented by the sample paths of a Brownian motion, and the cumulative charge distribution along a polymer is modeled by a realization of a Brownian bridge. Charges interact through a general positive-definite two-body potential. We study the infinite volume free energy density for a fixed realization of the Brownian motion; this is not self-averaging, but shows on the contrary a sample dependence through the local time of the Brownian motion. We obtain an explicit series representation for the free energy density; this has a finite radius of convergence, but the free energy is nevertheless analytic in the inverse temperature in the physical domain.
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