PreprintarXiv licencearXiv
Observable diameter of product measures with a power-type interior zero
Abstract
We determine the asymptotic order of the observable diameter of ℓp-product spaces associated with a probability measure on [0,1] whose density has a power-type interior zero. Different vanishing orders are allowed on the two sides of the zero. For every 1 ≤ p ≤ ∞, we obtain sharp two-sided estimates and show that the asymptotic order is governed by the larger of the two vanishing orders. In the case p=2, the transition occurs exactly at the threshold for the spectral gap.
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BibTeX
@misc{shioya2026observable,
title = {{Observable diameter of product measures with a power-type interior zero}},
author = {Takashi Shioya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35889},
eprint = {2610.35889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35889},
}
RIS
TY - UNPB
TI - Observable diameter of product measures with a power-type interior zero
AU - Takashi Shioya
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.35889
UR - https://arxiv.org/abs/2610.35889
AB - We determine the asymptotic order of the observable diameter of ℓ^p-product spaces associated with a probability measure on [0,1] whose density has a power-type interior zero. Different vanishing orders are allowed on the two sides of the zero. For every 1 ≤ p ≤ ∞, we obtain sharp two-sided estimates and show that the asymptotic order is governed by the larger of the two vanishing orders. In the case p=2, the transition occurs exactly at the threshold for the spectral gap.
ER -