Derives McDiarmid-type inequalities for dependent variables via approximate tensorization of entropy, with applications improving DKW rates to 1/sqrt(n) under weak dependence for log-concave measures.
On the Subgaussianity of Quantized Linear Maps: An AI-Assisted Note
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abstract
This short note presents a dimension-independent subgaussian concentration bound for Gaussian vectors under coordinate-wise nonlinear mappings. Discovered by Gemini 3.5 Flash, this result applies to any bounded function under a well-conditioned covariance. We apply this tool to answer a question of Simone Bombari on sign-quantized linear maps $Y = \text{sgn}(Wx)$.
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On McDiarmid's Inequality under Dependence via Approximate Tensorization of Entropy
Derives McDiarmid-type inequalities for dependent variables via approximate tensorization of entropy, with applications improving DKW rates to 1/sqrt(n) under weak dependence for log-concave measures.