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For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random variables. Frameworks and techniques vary from jackknives through semigroups and beyond. Some new applications are presented, in particular, recovering and improving upon all the known estimates on the variance of the length of the longest common subsequences of two random words.

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Variance Bounds: Some Old and Some New

  • 会议论文

  • 发表日期：

    2026年

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  • Clément Deslandes,
  • Christian Houdré

摘要

For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random variables. Frameworks and techniques vary from jackknives through semigroups and beyond. Some new applications are presented, in particular, recovering and improving upon all the known estimates on the variance of the length of the longest common subsequences of two random words.