PreprintCC BY 4.0arXiv
On the ℓ2 distortion of random triangulations
Abstract
For each n ∈ N, let Tn be a uniformly random (rooted, Type I) triangulation of the sphere with n vertices, viewed as a metric space equipped with its graph distance. We show that for every δ>0, with probability tending to $1$ as n → ∞, every embedding of Tn into a separable Hilbert space has distortion at least (log n)1/4−δ.
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BibTeX
@misc{miller2026ℓ2,
title = {{On the $\ell^2$ distortion of random triangulations}},
author = {Jason Miller and Julian Ransford and Fredy Yip},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40138},
eprint = {2609.40138},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40138},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the ℓ^2 distortion of random triangulations
AU - Jason Miller
AU - Julian Ransford
AU - Fredy Yip
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40138
UR - https://arxiv.org/abs/2609.40138
AB - For each n ∈ N, let T_n be a uniformly random (rooted, Type I) triangulation of the sphere with n vertices, viewed as a metric space equipped with its graph distance. We show that for every δ>0, with probability tending to $1$ as n → ∞, every embedding of T_n into a separable Hilbert space has distortion at least (log n)^1/4−δ.
ER -