Abstract
We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length J taking values in . Our main result states that the effective radius of the polymer is approximately ; evidently for large J the polymer undergoes stretching. This contrasts with the equilibrium situation without the time variable, where many earlier results show that the effective radius is approximately J.
For such a moving polymer taking values in , we offer a conjecture that the effective radius is approximately .
Funding Statement
The work of Carl Mueller is partially supported by the Simons grant 513424.
Acknowledgments
We are very grateful to the Associate Editor and to the anonymous referees for careful reading of the manuscript and for a number of useful comments and suggestions that significantly improved this paper.
The authors have no conflicts of interest to declare that are relevant to the content of this article.
Citation
Carl Mueller. Eyal Neuman. "Scaling properties of a moving polymer." Ann. Appl. Probab. 32 (6) 4251 - 4278, December 2022. https://doi.org/10.1214/22-AAP1785
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