arXiv:2610.35889v1 Announce Type: new 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.
Continue to arXiv Mathematics →You are being forwarded in 6s — stay on this page