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Convergence of rescaled “true” self-avoiding walks to the Tóth-Werner “true” self-repelling motion

Elena Kosygina & Jonathon Peterson

Electronic Journal of Probability2026https://doi.org/10.1214/26-ejp1489article
ABDC A
Weight
0.37

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.

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https://doi.org/https://doi.org/10.1214/26-ejp1489

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@article{elena2026,
  title        = {{Convergence of rescaled “true” self-avoiding walks to the Tóth-Werner “true” self-repelling motion}},
  author       = {Elena Kosygina & Jonathon Peterson},
  journal      = {Electronic Journal of Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/26-ejp1489},
}

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Convergence of rescaled “true” self-avoiding walks to the Tóth-Werner “true” self-repelling motion

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Evidence weight

0.37

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.16 × 0.4 = 0.06
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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