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- Self-repelling fractional Brownian motion : a generalized Edwards model for chain polymersPublication . Bornales, Jinky; Oliveira, Maria João; Streit, LudwigWe present an extension of the Edwards model for conformations of individual chain molecules in solvents in terms of fractional Brownian motion, and discuss the excluded volume effect on the end-to-end length of such trajectories or molecules.
- Intersection local times of independent Brownian motions as generalized white noise functionalsPublication . Albeverio, Sergio; Oliveira, Maria João; Streit, LudwigA "chaos expansion" of the intersection local time functional of two independent Brownian motions in Rd is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their Lp-properties are discussed. An important tool for deriving the chaos expansion is a computation of the "S-transform" of the corresponding regularized intersection local times and a control about their singular limit.
- Self-avoiding fractional Brownian motion: the Edwards modelPublication . Grothaus, Martin; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigIn this work we extend Varadhan’s construction of the Edwards polymer model to the case of fractional Brownian motions in Rd , for any dimension d ≥ 2, with arbitrary Hurst parameters H ≤ 1/d.
- Fractional Brownian polymers : some first resultsPublication . Bornales, Jinky; Eleutério, Samuel; Oliveira, Maria João; Streit, LudwigRecently the Edwards model for chain polymers in good solvents has been extended to include fractional Brownian motion trajectories as a description of polymer conformations. This raises in particular the question of the corresponding Flory formula for the end-to-end length of those molecules. A generalized Flory formula has been proposed, and there are some first results of numerical validations.