Convergence of rescaled “true” self-avoiding walks to the Tóth-Werner “true” self-repelling motion
Abstract
We prove that the rescaled “true” self-avoiding walk (n−2∕3X⌊nt⌋)t∈R+ converges weakly as n goes to infinity to the “true” self-repelling motion constructed by Tóth and Werner [35]. The proof features a joint generalized Ray-Knight theorem for the rescaled local times processes and their merge and absorption points as the main tool for showing both the tightness and convergence of the finite dimensional distributions. Thus, our result can be seen as an example of establishing a functional limit theorem for a family of processes by inverting the joint generalized Ray-Knight theorem.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Random Matrices and Applications
Diffusion and Search Dynamics
Publication details
- Journal / source
- Electronic Journal of Probability
- Publisher
- Institute of Mathematical Statistics
- Volume
- 31
- Issue
- none
- Publication date
- 1 January 2026