Brownian and fractional polymers with self-repulsion

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Brownian and fractional processes are useful computational tools for the modeling of physical phenomena. Here, modeling linear homopolymers in a solution as Brownian or fractional processes, we develop a formalism to take into account both the interactions of the polymer with the solvent as well as the effect of arbitrary polymer-polymer potentials and Gibbs factors. As an example, the average squared length is computed for a non-trivial Gaussian Gibbs factor, which is also compared with the Edwards' and step factor.