Weak uniqueness and autonomous approximation for the SLE-reversible Weil-Petersson response diffusion
Abstract
We study the self-consistent common-noise equation associated with the Weil--Petersson response differential of the rotationally marked SLE welding probability. For 0<κ≤4, we prove joint weak uniqueness among continuous adapted weak solutions whose law at each deterministic time is the welding probability, and obtain the Markov property in the original filtration. A conditional Gaussian lift and capacity localization give the required L1 generator-range density. Identification with the canonical law gives stationarity and reversibility. We also construct autonomous Fejér and Poisson regularizations with pathwise-unique global strong solutions. Their joint state-noise laws converge to the canonical law for every initial probability absolutely continuous with respect to the welding probability.
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BibTeX
@misc{cai2026weak,
title = {{Weak uniqueness and autonomous approximation for the SLE-reversible Weil-Petersson response diffusion}},
author = {Chunhao Cai},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04417},
eprint = {2611.04417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04417},
}
RIS
TY - UNPB
TI - Weak uniqueness and autonomous approximation for the SLE-reversible Weil-Petersson response diffusion
AU - Chunhao Cai
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04417
UR - https://arxiv.org/abs/2611.04417
AB - We study the self-consistent common-noise equation associated with the Weil--Petersson response differential of the rotationally marked SLE welding probability. For 0<κ≤4, we prove joint weak uniqueness among continuous adapted weak solutions whose law at each deterministic time is the welding probability, and obtain the Markov property in the original filtration. A conditional Gaussian lift and capacity localization give the required L^1 generator-range density. Identification with the canonical law gives stationarity and reversibility. We also construct autonomous Fejér and Poisson regularizations with pathwise-unique global strong solutions. Their joint state-noise laws converge to the canonical law for every initial probability absolutely continuous with respect to the welding probability.
ER -