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Lower Bounds on the Generalized Central Moments of the Optimal Alignments Score of Random Sequences

Author

Listed:
  • Ruoting Gong

    (Illinois Institute of Technology)

  • Christian Houdré

    (Georgia Institute of Technology)

  • Jüri Lember

    (University of Tartu)

Abstract

We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained under a main assumption for which sufficient conditions are provided. When the main assumption fails, we nevertheless develop a “uniform approximation” method leading to asymptotic lower bounds. Our general results are then applied to the length of the longest common subsequences of binary strings, in which case asymptotic lower bounds are obtained for the moments and the exponential moments of the optimal score. As a by-product, a local upper bound on the rate function associated with the length of the longest common subsequences of two binary strings is also obtained.

Suggested Citation

  • Ruoting Gong & Christian Houdré & Jüri Lember, 2018. "Lower Bounds on the Generalized Central Moments of the Optimal Alignments Score of Random Sequences," Journal of Theoretical Probability, Springer, vol. 31(2), pages 643-683, June.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:2:d:10.1007_s10959-016-0730-4
    DOI: 10.1007/s10959-016-0730-4
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