Summary
We consider a system that models the shape of a growing polymer. Our basic problem concerns the asymptotic behavior ofX t , the location of the end of the polymer at timet. We obtain bounds onX t in the (physically uninteresting) case thatd=1 and the interaction functionf(x)≥0. If, in addition,f(x) behaves for largex likeCx −β with β<1 we obtain a strong law that gives the exact growth rate.
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Partially supported by the National Science Foundation and the Army Research Office through the Mathematical Sciences Institute (MSI) at Cornell University
Partially supported by SERC grant GR/G02307 and MSI, this work was done while the second author was visiting Cornell, April–July, 1990
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Durrett, R.T., Rogers, L.C.G. Asymptotic behavior of Brownian polymers. Probab. Th. Rel. Fields 92, 337–349 (1992). https://doi.org/10.1007/BF01300560
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DOI: https://doi.org/10.1007/BF01300560