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2021 On the limiting law of the length of the longest common and increasing subsequences in random words with arbitrary distribution
Clément Deslandes, Christian Houdré
Author Affiliations +
Electron. J. Probab. 26: 1-27 (2021). DOI: 10.1214/21-EJP612

Abstract

Let (Xk)k1 and (Yk)k1 be two independent sequences of i.i.d. random variables, with values in a finite and totally ordered alphabet Am:={1,,m}, m2, having respective probability mass function p1X,,pmX and p1Y,,pmY. Let LCIn be the length of the longest common and weakly increasing subsequences in X1,...,Xn and Y1,...,Yn. Once properly centered and normalized, LCIn is shown to have a limiting distribution which is expressed as a functional of two independent multidimensional Brownian motions.

Funding Statement

Research supported in part by the grant ♯524678 from the Simons Foundation.

Acknowledgments

We sincerely thank an Associate Editor and a referee for their detailed readings and numerous comments which greatly helped to improve this manuscript.

Citation

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Clément Deslandes. Christian Houdré. "On the limiting law of the length of the longest common and increasing subsequences in random words with arbitrary distribution." Electron. J. Probab. 26 1 - 27, 2021. https://doi.org/10.1214/21-EJP612

Information

Received: 3 September 2019; Accepted: 29 March 2021; Published: 2021
First available in Project Euclid: 18 May 2021

arXiv: 1906.06544
Digital Object Identifier: 10.1214/21-EJP612

Subjects:
Primary: 05A05, 60C05, 60F05

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