jl-lemma-chi-square-concentration-proof

OUT premise — summaries/2026/08/24/wiki-JohnsonE28093Lindenstrauss_lemma-chunk-1.md

Created 2026-08-24T17:11:13+00:00

The classical JL proof uses the fact that for A ~ 𝒩(0,1)^{k×n}, the ratio ‖Ax‖²/‖x‖² follows a χ²(k) distribution, yielding the concentration bound Pr(r ∈ (1±ε)·k) ≥ 1 − 2·exp(−(k/2)·(ε²/2 − ε³/3)).