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The Polynomially Self-repelling Motion
Abstract
[Kosygina et al. 2023] showed that the rescaled polynomially self-repelling walk does not converge to any Brownian motion perturbed at extrema (BMPE). Motivated by this result, we introduce an explicit candidate for the scaling limit, the polynomially self-repelling motion (PSRM), and study its properties. The construction relies on a new family of continuous stochastic flows, called polynomially self-repelling flows, introduced in [Yu 2026]. A key ingredient in relating the limiting process of the rescaled walk to the PSRM is a joint Ray-Knight theorem for rescaled local time processes, extending the classical Ray-Knight theorems of [Tóth 1996].
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BibTeX
@misc{yu2026polynomially,
title = {{The Polynomially Self-repelling Motion}},
author = {Yaolin Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38591},
eprint = {2610.38591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38591},
}
RIS
TY - UNPB
TI - The Polynomially Self-repelling Motion
AU - Yaolin Yu
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38591
UR - https://arxiv.org/abs/2610.38591
AB - [Kosygina et al. 2023] showed that the rescaled polynomially self-repelling walk does not converge to any Brownian motion perturbed at extrema (BMPE). Motivated by this result, we introduce an explicit candidate for the scaling limit, the polynomially self-repelling motion (PSRM), and study its properties. The construction relies on a new family of continuous stochastic flows, called polynomially self-repelling flows, introduced in [Yu 2026]. A key ingredient in relating the limiting process of the rescaled walk to the PSRM is a joint Ray-Knight theorem for rescaled local time processes, extending the classical Ray-Knight theorems of [Tóth 1996].
ER -