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2018 Monotonous subsequences and the descent process of invariant random permutations
Mohamed Slim Kammoun
Electron. J. Probab. 23(none): 1-31 (2018). DOI: 10.1214/18-EJP244


It is known from the work of Baik, Deift and Johansson [3] that we have Tracy-Widom fluctuations for the longest increasing subsequence of uniform permutations. In this paper, we prove that this result holds also in the case of the Ewens distribution and more generally for a class of random permutations with distribution invariant under conjugation. Moreover, we obtain the convergence of the first components of the associated Young tableaux to the Airy Ensemble as well as the global convergence to the Vershik-Kerov-Logan-Shepp shape. Using similar techniques, we also prove that the limiting descent process of a large class of random permutations is stationary, one-dependent and determinantal.


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Mohamed Slim Kammoun. "Monotonous subsequences and the descent process of invariant random permutations." Electron. J. Probab. 23 1 - 31, 2018.


Received: 11 June 2018; Accepted: 11 November 2018; Published: 2018
First available in Project Euclid: 27 November 2018

zbMATH: 07021674
MathSciNet: MR3885551
Digital Object Identifier: 10.1214/18-EJP244

Primary: 60C05


Vol.23 • 2018
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