December 2022 Scaling properties of a moving polymer
Carl Mueller, Eyal Neuman
Author Affiliations +
Ann. Appl. Probab. 32(6): 4251-4278 (December 2022). DOI: 10.1214/22-AAP1785


We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length J taking values in (0,). Our main result states that the effective radius of the polymer is approximately J5/3; 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 R2, we offer a conjecture that the effective radius is approximately J5/4.

Funding Statement

The work of Carl Mueller is partially supported by the Simons grant 513424.


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.


Download Citation

Carl Mueller. Eyal Neuman. "Scaling properties of a moving polymer." Ann. Appl. Probab. 32 (6) 4251 - 4278, December 2022.


Received: 1 January 2021; Revised: 1 September 2021; Published: December 2022
First available in Project Euclid: 6 December 2022

MathSciNet: MR4522351
zbMATH: 1504.60102
Digital Object Identifier: 10.1214/22-AAP1785

Primary: 60H15
Secondary: 82D60

Keywords: heat equation , Polymer , scaling , Stochastic partial differential equations , White noise

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.32 • No. 6 • December 2022
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