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The norm of a Gaussian vector

The distribution of ‖X‖₂ for X ~ N(0, I_d) as the dimension grows, against the √d prediction.

High-Dim Probabilityconcentrationgaussianhigh dimensionnorm

The mathematics behind this

High-Dimensional Geometry and Concentration of the Norm
Why a Gaussian vector lives on a thin shell, why random directions are nearly orthogonal, and why almost all of a sphere's volume sits near any equator.

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