Mock-Gaussian behaviour

Research output: Chapter in Book/Report/Conference proceedingChapter

Standard

Mock-Gaussian behaviour. / Hughes, Christopher; Mezzadri, F. (Editor); Snaith, N. C. (Editor).

Recent Perspectives in Random Matrix Theory and Number Theory. Vol. 322 Cambridge University Press, 2005. p. 337-355 (London Mathematical Society lecture Note Series).

Research output: Chapter in Book/Report/Conference proceedingChapter

Harvard

Hughes, C, Mezzadri, F (ed.) & Snaith, NC (ed.) 2005, Mock-Gaussian behaviour. in Recent Perspectives in Random Matrix Theory and Number Theory. vol. 322, London Mathematical Society lecture Note Series, Cambridge University Press, pp. 337-355.

APA

Hughes, C., Mezzadri, F. (Ed.), & Snaith, N. C. (Ed.) (2005). Mock-Gaussian behaviour. In Recent Perspectives in Random Matrix Theory and Number Theory (Vol. 322, pp. 337-355). (London Mathematical Society lecture Note Series). Cambridge University Press.

Vancouver

Hughes C, Mezzadri F, (ed.), Snaith NC, (ed.). Mock-Gaussian behaviour. In Recent Perspectives in Random Matrix Theory and Number Theory. Vol. 322. Cambridge University Press. 2005. p. 337-355. (London Mathematical Society lecture Note Series).

Author

Hughes, Christopher ; Mezzadri, F. (Editor) ; Snaith, N. C. (Editor). / Mock-Gaussian behaviour. Recent Perspectives in Random Matrix Theory and Number Theory. Vol. 322 Cambridge University Press, 2005. pp. 337-355 (London Mathematical Society lecture Note Series).

Bibtex - Download

@inbook{dbe986d85fc04bcd8890f4afbb5ecc67,
title = "Mock-Gaussian behaviour",
abstract = "We show that the moments of the smooth counting function of a set of points encodes the same information as the $n$-level density of these points. If the points are the eigenvalues of matrices taken from the classical compact groups with Haar measure, then we show that the first few moments of the smooth counting function are Gaussian, while the distribution is not. The same phenomenon occurs for smooth counting functions of the zeros of $L$--functions, and we give examples relating to each classical compact group. The advantage of calculating moments of the counting function is that combinatorially, they are far easier to handle than the $n$-level densities.",
keywords = "Pure Mathematics",
author = "Christopher Hughes and F. Mezzadri and Snaith, {N. C.}",
year = "2005",
month = "7",
language = "English",
isbn = "9780521620581",
volume = "322",
series = "London Mathematical Society lecture Note Series",
publisher = "Cambridge University Press",
pages = "337--355",
booktitle = "Recent Perspectives in Random Matrix Theory and Number Theory",

}

RIS (suitable for import to EndNote) - Download

TY - CHAP

T1 - Mock-Gaussian behaviour

AU - Hughes, Christopher

A2 - Mezzadri, F.

A2 - Snaith, N. C.

PY - 2005/7

Y1 - 2005/7

N2 - We show that the moments of the smooth counting function of a set of points encodes the same information as the $n$-level density of these points. If the points are the eigenvalues of matrices taken from the classical compact groups with Haar measure, then we show that the first few moments of the smooth counting function are Gaussian, while the distribution is not. The same phenomenon occurs for smooth counting functions of the zeros of $L$--functions, and we give examples relating to each classical compact group. The advantage of calculating moments of the counting function is that combinatorially, they are far easier to handle than the $n$-level densities.

AB - We show that the moments of the smooth counting function of a set of points encodes the same information as the $n$-level density of these points. If the points are the eigenvalues of matrices taken from the classical compact groups with Haar measure, then we show that the first few moments of the smooth counting function are Gaussian, while the distribution is not. The same phenomenon occurs for smooth counting functions of the zeros of $L$--functions, and we give examples relating to each classical compact group. The advantage of calculating moments of the counting function is that combinatorially, they are far easier to handle than the $n$-level densities.

KW - Pure Mathematics

M3 - Chapter

SN - 9780521620581

VL - 322

T3 - London Mathematical Society lecture Note Series

SP - 337

EP - 355

BT - Recent Perspectives in Random Matrix Theory and Number Theory

PB - Cambridge University Press

ER -