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

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

2008-12-18

arxiv.org/abs/0812.3672v3

Bernoulli 2010, Vol. 16, No. 2, 471-492

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/09-BEJ218 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ218

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.

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