Jiaming Xu

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math.PR2026

Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d > n$ Regime

Hang Du, Cheng Mao, Nike Sun +2

A random geometric graph (RGG) is generated by first sampling latent points $x_{1}, \dots, x_{n}$ independently and uniformly from the unit sphere in $R^{d}$ , and then connecting…

math.PR2026

Random geometric graphs with smooth kernels: sharp detection threshold and a spectral conjecture

Cheng Mao, Yihong Wu, Jiaming Xu

A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_{1}, \dots, x_{n}$ independently and uniformly from the $d$ -dimensional unit sphere, the…

Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the d>n Regime

Random geometric graphs with smooth kernels: sharp detection threshold and a spectral conjecture

Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d > n$ Regime