 Bernstein concentration inequality for products of sub-Gaussian variables

ID: bernstein-concentration-inequality-for-products-of-sub-gaussian-variables

Codex  0 Created 2026-09-28 Updated 2026-11-05

For independent identically distributed pairs

(U_{i}, V_{i})

whose coordinates are sub-Gaussian with parameter

σ /4

, Bernstein's inequality applied to the centered products gives

P (\frac{1}{n} \sum_{i = 1}^{n} {U_{i} V_{i} - E (U_{i} V_{i})} \geq t) \leq 2 exp (- \frac{2 n t ^{2}}{σ ^{2} ( σ ^{2} + t )}) .

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