December 2023 The effective radius of self repelling elastic manifolds
Carl Mueller, Eyal Neuman
Author Affiliations +
Ann. Appl. Probab. 33(6B): 5668-5692 (December 2023). DOI: 10.1214/23-AAP1956


We study elastic manifolds with self-repelling terms and estimate their effective radius. This class of manifolds is modelled by a self-repelling vector-valued Gaussian free field with Neumann boundary conditions over the domain [N,N]dZd, that takes values in Rd. Our main result states that in two dimensions (d=2), the effective radius RN of the manifold is approximately N. This verifies the conjecture of Kantor, Kardar and Nelson (Phys. Rev. Lett. 58 (1987) 1289–1292) up to a logarithmic correction. Our results in d3 give a similar lower bound on RN and an upper of order Nd/2. This result implies that self-repelling elastic manifolds undergo a substantial stretching at any dimension.

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.


Download Citation

Carl Mueller. Eyal Neuman. "The effective radius of self repelling elastic manifolds." Ann. Appl. Probab. 33 (6B) 5668 - 5692, December 2023.


Received: 1 December 2021; Revised: 1 July 2022; Published: December 2023
First available in Project Euclid: 13 December 2023

MathSciNet: MR4677742
Digital Object Identifier: 10.1214/23-AAP1956

Primary: 60G60
Secondary: 60G15

Keywords: elastic manifold , Gaussian free field , self-avoiding

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.33 • No. 6B • December 2023
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