Year: 2026
Type: preprint
Abstract: We determine the asymptotic order of the observable diameter of $\ell^p$-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 $1 \le p \le \infty$, 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.
Source: arXiv (Cornell University)
Author: Shioya, Takashi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 距離空間と測度距離空間の幾何学
OpenAlex ID: W7224101077