Asymptotics for random Young diagrams when the word length and alphabet size simultaneously grow to infinity

Abstract

Given a random word of size $n$ whose letters are drawn independently from an ordered alphabet of size $m$, the fluctuations of the shape of the random RSK Young tableaux are investigated, when $n$ and $m$ converge together to infinity. If $m$ does not grow too fast and if the draws are uniform, then the limiting shape is the same as the limiting spectrum of the GUE. In the non-uniform case, a control of both highest probabilities will ensure the convergence of the first row of the tableau toward the Tracy--Widom distribution.

Published in at http://dx.doi.org/10.3150/09-BEJ218 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (2)

• On the Limiting Shape of Markovian Random Young Tableaux
• On the Limiting Shape of Young Tableaux Associated With Inhomogeneous Random Words

Cited by in corpus (6)

• Multi-state asymmetric simple exclusion processes
• On the limiting law of the length of the longest common and increasing subsequences in random words
• On the rate of approximation in finite-alphabet longest increasing subsequence problems
• On the Limiting Shape of Young Tableaux Associated With Inhomogeneous Random Words
• Longest common subsequences between words of very unequal length
• Simultaneous large deviations for the shape of Young diagrams associated with random words