Let and be two independent sequences of i.i.d. random variables, with values in a finite and totally ordered alphabet , , having respective probability mass function and . Let be the length of the longest common and weakly increasing subsequences in and . Once properly centered and normalized, is shown to have a limiting distribution which is expressed as a functional of two independent multidimensional Brownian motions.
Research supported in part by the grant ♯524678 from the Simons Foundation.
We sincerely thank an Associate Editor and a referee for their detailed readings and numerous comments which greatly helped to improve this manuscript.
"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