Probability Theory and Related Fields

, Volume 92, Issue 3, pp 337–349 | Cite as

Asymptotic behavior of Brownian polymers

  • R. T. Durrett
  • L. C. G. Rogers


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.


Polymer Growth Rate Stochastic Process Asymptotic Behavior Probability Theory 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • R. T. Durrett
    • 1
  • L. C. G. Rogers
    • 2
  1. 1.Mathematics DepartmentCornell UniversityIthacaUSA
  2. 2.Queen Mary and Westfied CollegeSchool of Mathematical SciencesLondonUK

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