The Characteristic Polynomial of a Random Permutation Matrix at Different Points

Dirk Zeindler; Kim Dang

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The Characteristic Polynomial of a Random Permutation Matrix at Different Points

Kim Dang, Dirk Zeindler

Probability · Submitted 20 Oct 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the behavior at different points is independent in the limit and are asymptotically normal.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.05 · states quantitative result 0.35 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enables us to study more general matrices, closely related to permutation matrices, and multiplicative class functions.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points.	contribution 0.83	0.78	0.05	unclear 0.52
s1	The permutations are chosen with respect to the Ewens distribution on the symmetric group.	method 0.91	0.35	0.02	asserted 0.97
s2	We show that the behavior at different points is independent in the limit and are asymptotically normal.	result 1.00	0.95	0.85	asserted 1.00
s3	Our methods enables us to study more general matrices, closely related to permutation matrices, and multiplicative class functions.	contribution 0.73	0.86	0.06	asserted 0.90

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enables us to study more general matrices, closely related to permutation matrices, and multiplicative class functions.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Second, we state CLT's for the logarithm of characteristic polynomials for matrix groups related to permutation matrices, such as some Weyl groups [ref] and of the wreath product $𝕋≀S_n$ [ref] , where $𝕋 = {z∈; |z| =1}$.

On averages of randomized class functions on the symmetric groups and their asymptotics · Introduction · 0.81

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