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Monotonous subsequences and the descent process of invariant random permutations

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Monotonous subsequences and the descent process of invariant random permutations. / Kammoun, Mohamed Slim.
In: Electronic Journal of Probability, Vol. 23, 30.11.2018, p. 1-31.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Kammoun, MS 2018, 'Monotonous subsequences and the descent process of invariant random permutations', Electronic Journal of Probability, vol. 23, pp. 1-31. https://doi.org/10.1214/18-ejp244

APA

Kammoun, M. S. (2018). Monotonous subsequences and the descent process of invariant random permutations. Electronic Journal of Probability, 23, 1-31. https://doi.org/10.1214/18-ejp244

Vancouver

Kammoun MS. Monotonous subsequences and the descent process of invariant random permutations. Electronic Journal of Probability. 2018 Nov 30;23:1-31. Epub 2018 Nov 27. doi: 10.1214/18-ejp244

Author

Kammoun, Mohamed Slim. / Monotonous subsequences and the descent process of invariant random permutations. In: Electronic Journal of Probability. 2018 ; Vol. 23. pp. 1-31.

Bibtex

@article{1abb46e43f5643c38f4e9b8676abf0c2,
title = "Monotonous subsequences and the descent process of invariant random permutations",
abstract = "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.",
keywords = "descent process, Determinantal point processes, Longest increasing subsequence, Random permutations, Robinson-Schensted correspondence, Tracy-Widom distribution",
author = "Kammoun, {Mohamed Slim}",
year = "2018",
month = nov,
day = "30",
doi = "10.1214/18-ejp244",
language = "English",
volume = "23",
pages = "1--31",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - Monotonous subsequences and the descent process of invariant random permutations

AU - Kammoun, Mohamed Slim

PY - 2018/11/30

Y1 - 2018/11/30

N2 - 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.

AB - 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.

KW - descent process

KW - Determinantal point processes

KW - Longest increasing subsequence

KW - Random permutations

KW - Robinson-Schensted correspondence

KW - Tracy-Widom distribution

U2 - 10.1214/18-ejp244

DO - 10.1214/18-ejp244

M3 - Journal article

VL - 23

SP - 1

EP - 31

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

ER -