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<p>We provide a simpler proof of a sharp concentration inequality for sub-Gaussian simple tensors obtained recently by Al-Ghattas, Chen, and Sanz-Alonso. Our approach uses a matrix deviation inequality for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell ^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> norms and a basic chaining argument.</p>

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On the Dimension-Free Concentration of Simple Tensors via Matrix Deviation

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Pedro Abdalla,
  • Roman Vershynin

摘要

We provide a simpler proof of a sharp concentration inequality for sub-Gaussian simple tensors obtained recently by Al-Ghattas, Chen, and Sanz-Alonso. Our approach uses a matrix deviation inequality for \(\ell ^p\) ℓ p norms and a basic chaining argument.