PreprintarXiv licencearXiv
Hopf quotients of the infinite-dimensional Gaussian pyramid
Abstract
We study the infinite-dimensional Gaussian pyramid and its quotients by the global sign flip and the U(1)-Hopf action. We resolve affirmatively a long-standing problem posed by Tomohiro Fukaya around 2014: these three limiting geometries are pairwise non-similar, meaning that no positive rescaling makes any two of them coincide.
Related
- The singular Gaussian scaling limit for a tagged particle in the infinite-dimensional Dyson model at β=2
- On the Onsager--Machlup functional of the infinite-dimensional angular central Gaussian distribution and related measures
- Constructive Universal Approximation by Infinite-Dimensional Neural Networks via Gaussian-Weighted Ridgelet Transform
- Quotients of graded quasi-Hopf algebras
- Sparsity for Infinite-Parametric Holomorphic Functions on Gaussian Spaces
BibTeX
@misc{shioya2026hopf,
title = {{Hopf quotients of the infinite-dimensional Gaussian pyramid}},
author = {Takashi Shioya and Shigeaki Yokota},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07030},
eprint = {2609.07030},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07030},
}
RIS
TY - UNPB
TI - Hopf quotients of the infinite-dimensional Gaussian pyramid
AU - Takashi Shioya
AU - Shigeaki Yokota
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.07030
UR - https://arxiv.org/abs/2609.07030
AB - We study the infinite-dimensional Gaussian pyramid and its quotients by the global sign flip and the U(1)-Hopf action. We resolve affirmatively a long-standing problem posed by Tomohiro Fukaya around 2014: these three limiting geometries are pairwise non-similar, meaning that no positive rescaling makes any two of them coincide.
ER -