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Central limit theorem for multiplicative class function on the symmetric group

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

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Central limit theorem for multiplicative class function on the symmetric group. / Zeindler, Dirk.
In: Journal of Theoretical Probability, Vol. 26, No. 4, 12.2013, p. 968-996.

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

Harvard

Zeindler, D 2013, 'Central limit theorem for multiplicative class function on the symmetric group', Journal of Theoretical Probability, vol. 26, no. 4, pp. 968-996. https://doi.org/10.1007/s10959-011-0382-3

APA

Zeindler, D. (2013). Central limit theorem for multiplicative class function on the symmetric group. Journal of Theoretical Probability, 26(4), 968-996. https://doi.org/10.1007/s10959-011-0382-3

Vancouver

Zeindler D. Central limit theorem for multiplicative class function on the symmetric group. Journal of Theoretical Probability. 2013 Dec;26(4):968-996. doi: 10.1007/s10959-011-0382-3

Author

Zeindler, Dirk. / Central limit theorem for multiplicative class function on the symmetric group. In: Journal of Theoretical Probability. 2013 ; Vol. 26, No. 4. pp. 968-996.

Bibtex

@article{7eee7d7f458843b2841be49080eeb10b,
title = "Central limit theorem for multiplicative class function on the symmetric group",
abstract = "Hambly, Keevash, O{\textquoteright}Connell, and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on the symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.",
keywords = "Symmetric group , Ewens measure, Characteristic polynomial , Multiplicative class function , Wasserstein distance",
author = "Dirk Zeindler",
year = "2013",
month = dec,
doi = "10.1007/s10959-011-0382-3",
language = "English",
volume = "26",
pages = "968--996",
journal = "Journal of Theoretical Probability",
issn = "1572-9230",
publisher = "Springer New York",
number = "4",

}

RIS

TY - JOUR

T1 - Central limit theorem for multiplicative class function on the symmetric group

AU - Zeindler, Dirk

PY - 2013/12

Y1 - 2013/12

N2 - Hambly, Keevash, O’Connell, and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on the symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.

AB - Hambly, Keevash, O’Connell, and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on the symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.

KW - Symmetric group

KW - Ewens measure

KW - Characteristic polynomial

KW - Multiplicative class function

KW - Wasserstein distance

U2 - 10.1007/s10959-011-0382-3

DO - 10.1007/s10959-011-0382-3

M3 - Journal article

VL - 26

SP - 968

EP - 996

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 1572-9230

IS - 4

ER -