Simultaneous Large Deviations for the Shape of Young Diagrams Associated With Random Words

Details Simultaneous Large Deviations for the Shape of Young Diagrams Associated With Random Words Simultaneous Large Deviations for the Shape of Young Diagrams Associated With Random Words

2011-10-04

arxiv.org/abs/1110.0804v1

Mathematics

Probability

Scientific paper

We investigate the large deviations of the shape of the random RSK Young tableaux 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 tableaux 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 tableau 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 tableaux, i.e., for the length of the longest increasing subsequence of the random word are also given for both models

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