High Dimensional Probability VIIOn the Order of the Central Moments of the Length of the Longest Common Subsequences in Random Words

High Dimensional Probability VII: On the Order of the Central Moments of the Length of the... [We investigate the order of the r-th, 1 ≤ r < +∞, central moment of the length of the longest common subsequences of two independent random words of size n whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, a lower bound is shown to be of order nr∕2. This result complements a generic upper bound also of order nr∕2.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

High Dimensional Probability VIIOn the Order of the Central Moments of the Length of the Longest Common Subsequences in Random Words

Part of the Progress in Probability Book Series (volume 71)
Editors: Houdré, Christian; Mason, David M.; Reynaud-Bouret, Patricia; Rosiński, Jan
31 pages

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References (14)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-40517-9
Pages
105 –136
DOI
10.1007/978-3-319-40519-3_5
Publisher site
See Chapter on Publisher Site

Abstract

[We investigate the order of the r-th, 1 ≤ r < +∞, central moment of the length of the longest common subsequences of two independent random words of size n whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, a lower bound is shown to be of order nr∕2. This result complements a generic upper bound also of order nr∕2.]

Published: Sep 22, 2016

Keywords: Burkholder inequality; Efron-Stein inequality; Last passage percolation; Longest common subsequence; r -th central moment

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