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