Author

Jiaming Xu

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Preprint Oct 2026

Sharp detection thresholds for random geometric graphs with polynomial average degrees

We study the random geometric graph formed by connecting $n$ independent uniform points on $\mathbb S^{d-1}$ whenever their inner product exceeds a threshold chosen to give edge density $p$. We establish the conjectured dimensionality threshold for indistinguishability from the Erd\"{o}s-R\'enyi graph $G(n,p)$ througho...

Hang Du, Cheng Mao, Ni-Ke Sun et al. · 0 citations

Jul 2026

High-Dimensional Procrustes Matching via Tree Counts

A polynomial-time algorithm for exact recovery at constant correlation of Gaussian vectors, and an improved information-theoretic guarantee, showing that exact recovery is possible when $\rho^2 \gtrsim \max\{\log n/d,\sqrt{\log n/n}\}$.

Xiaochun Niu, T. Schramm, Jiaming Xu · arXiv.org · 0 citations