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Article Dans Une Revue Markov Processes And Related Fields Année : 2015

GUE minors, maximal Brownian functionals and longest increasing subsequences

Résumé

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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Dates et versions

hal-00917273 , version 1 (11-12-2013)
hal-00917273 , version 2 (11-06-2014)
hal-00917273 , version 3 (17-11-2014)
hal-00917273 , version 4 (26-11-2014)

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