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Almost sure weak convergence for the circular ensembles of Dyson.

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

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Almost sure weak convergence for the circular ensembles of Dyson. / Blower, Gordon.
In: Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports, Vol. 75, No. 6, 2003, p. 425-433.

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

Harvard

Blower, G 2003, 'Almost sure weak convergence for the circular ensembles of Dyson.', Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports, vol. 75, no. 6, pp. 425-433. https://doi.org/10.1080/10451120310001641126

APA

Blower, G. (2003). Almost sure weak convergence for the circular ensembles of Dyson. Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports, 75(6), 425-433. https://doi.org/10.1080/10451120310001641126

Vancouver

Blower G. Almost sure weak convergence for the circular ensembles of Dyson. Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports. 2003;75(6):425-433. doi: 10.1080/10451120310001641126

Author

Blower, Gordon. / Almost sure weak convergence for the circular ensembles of Dyson. In: Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports. 2003 ; Vol. 75, No. 6. pp. 425-433.

Bibtex

@article{e36b68e99f5b487899c94ea89b4a86dd,
title = "Almost sure weak convergence for the circular ensembles of Dyson.",
abstract = "The circular ensembles of Dyson satisfy isoperimetric inequalities and concentration of measure phenomena for large particle numbers analogous to the isoperimetric inequality for surface measure on the sphere in Euclidean space of high dimension. This leads to a geometrical proof of a result of Johansson [Bull. Sci. Math. (2) 112, (1988), 257-304] that the empirical distribution of energy levels under such ensembles converge weakly almost surely to normalized arclength on the unit circle as n→∞.",
keywords = "Random matrices, Isoperimetric inequality, Statistical mechanics, Circular ensembles, Primary, 60K35, Secondary, 47B06",
author = "Gordon Blower",
year = "2003",
doi = "10.1080/10451120310001641126",
language = "English",
volume = "75",
pages = "425--433",
journal = "Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports",
issn = "1744-2508",
publisher = "Gordon and Breach Science Publishers",
number = "6",

}

RIS

TY - JOUR

T1 - Almost sure weak convergence for the circular ensembles of Dyson.

AU - Blower, Gordon

PY - 2003

Y1 - 2003

N2 - The circular ensembles of Dyson satisfy isoperimetric inequalities and concentration of measure phenomena for large particle numbers analogous to the isoperimetric inequality for surface measure on the sphere in Euclidean space of high dimension. This leads to a geometrical proof of a result of Johansson [Bull. Sci. Math. (2) 112, (1988), 257-304] that the empirical distribution of energy levels under such ensembles converge weakly almost surely to normalized arclength on the unit circle as n→∞.

AB - The circular ensembles of Dyson satisfy isoperimetric inequalities and concentration of measure phenomena for large particle numbers analogous to the isoperimetric inequality for surface measure on the sphere in Euclidean space of high dimension. This leads to a geometrical proof of a result of Johansson [Bull. Sci. Math. (2) 112, (1988), 257-304] that the empirical distribution of energy levels under such ensembles converge weakly almost surely to normalized arclength on the unit circle as n→∞.

KW - Random matrices

KW - Isoperimetric inequality

KW - Statistical mechanics

KW - Circular ensembles

KW - Primary

KW - 60K35

KW - Secondary

KW - 47B06

U2 - 10.1080/10451120310001641126

DO - 10.1080/10451120310001641126

M3 - Journal article

VL - 75

SP - 425

EP - 433

JO - Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports

JF - Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports

SN - 1744-2508

IS - 6

ER -