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Asymptotic behavior of Brownian polymers
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  • Published: September 1992

Asymptotic behavior of Brownian polymers

  • R. T. Durrett1 &
  • L. C. G. Rogers2 

Probability Theory and Related Fields volume 92, pages 337–349 (1992)Cite this article

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  • 43 Citations

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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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Author information

Authors and Affiliations

  1. Mathematics Department, Cornell University, White Hall, 14853, Ithaca, NY, USA

    R. T. Durrett

  2. Queen Mary and Westfied College, School of Mathematical Sciences, Mile End Road, El 4NS, London, UK

    L. C. G. Rogers

Authors
  1. R. T. Durrett
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  2. L. C. G. Rogers
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Additional information

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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Cite this article

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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  • Received: 03 May 1991

  • Revised: 11 November 1991

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01300560

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Keywords

  • Polymer
  • Growth Rate
  • Stochastic Process
  • Asymptotic Behavior
  • Probability Theory
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