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August 2015 Simultaneous large deviations for the shape of Young diagrams associated with random words
Christian Houdré, Jinyong Ma
Bernoulli 21(3): 1494-1537 (August 2015). DOI: 10.3150/14-BEJ612

Abstract

We investigate the large deviations of the shape of the random RSK Young diagrams associated with a random word of size $n$ whose letters are independently drawn from an alphabet of size $m=m(n)$. When the letters are drawn uniformly and when both $n$ and $m$ converge together to infinity, $m$ not growing too fast with respect to $n$, the large deviations of the shape of the Young diagrams are shown to be the same as that of the spectrum of the traceless GUE. In the non-uniform case, a control of both highest probabilities will ensure that the length of the top row of the diagram satisfies a large deviation principle. In either case, both speeds and rate functions are identified. To complete our study, non-asymptotic concentration bounds for the length of the top row of the diagrams, that is, for the length of the longest increasing subsequence of the random word are also given for both models.

Citation

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Christian Houdré. Jinyong Ma. "Simultaneous large deviations for the shape of Young diagrams associated with random words." Bernoulli 21 (3) 1494 - 1537, August 2015. https://doi.org/10.3150/14-BEJ612

Information

Received: 1 December 2011; Revised: 1 December 2013; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1330.60048
MathSciNet: MR3352052
Digital Object Identifier: 10.3150/14-BEJ612

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 3 • August 2015
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