GUE minors, maximal Brownian functionals and longest increasing subsequences

Abstract : We present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. In turn, these results allow to recover the limiting shape (properly centered and scaled) of the RSK Young diagrams associated with a random word as a function of the spectra of these minors. Since the length of the top row of the diagrams is the length of the longest increasing subsequence of the random word, the corresponding limiting law also follows.
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Article dans une revue
Markov Processes and Related Fields, Polymath, 2015, 21, pp.109-126
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https://hal.archives-ouvertes.fr/hal-00917273
Contributeur : Florent Benaych-Georges <>
Soumis le : mercredi 26 novembre 2014 - 09:27:35
Dernière modification le : mardi 11 octobre 2016 - 12:02:54
Document(s) archivé(s) le : vendredi 27 février 2015 - 10:58:05

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  • HAL Id : hal-00917273, version 4
  • ARXIV : 1312.3301

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Florent Benaych-Georges, Christian Houdré. GUE minors, maximal Brownian functionals and longest increasing subsequences. Markov Processes and Related Fields, Polymath, 2015, 21, pp.109-126. <hal-00917273v4>

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