Geodesic
Self-similarity in the circular unitary ensemble
Discrete analysis (2016) Cet article a éte moissonné depuis la source Scholastica

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This paper gives a rigorous proof of a conjectured statistical self-similarity property of the eigenvalues random matrices from the Circular Unitary Ensemble. We consider on the one hand the eigenvalues of an $n \times n$ CUE matrix, and on the other hand those eigenvalues $e^{iφ}$ of an $mn \times mn$ CUE matrix with $|φ| \le π/ m$, rescaled to fill the unit circle. We show that for a large range of mesoscopic scales, these collections of points are statistically indistinguishable for large $n$. The proof is based on a comparison theorem for determinantal point processes which may be of independent interest.
Publié le : 
@article{DAS_2016_a10,
     author = {Elizabeth S. Meckes and Mark W. Meckes},
     title = {Self-similarity in the circular unitary ensemble},
     journal = {Discrete analysis},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2016_a10/}
}
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AU  - Elizabeth S. Meckes
AU  - Mark W. Meckes
TI  - Self-similarity in the circular unitary ensemble
JO  - Discrete analysis
PY  - 2016
UR  - http://geodesic.mathdoc.fr/item/DAS_2016_a10/
LA  - en
ID  - DAS_2016_a10
ER  - 
%0 Journal Article
%A Elizabeth S. Meckes
%A Mark W. Meckes
%T Self-similarity in the circular unitary ensemble
%J Discrete analysis
%D 2016
%U http://geodesic.mathdoc.fr/item/DAS_2016_a10/
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%F DAS_2016_a10
Elizabeth S. Meckes; Mark W. Meckes. Self-similarity in the circular unitary ensemble. Discrete analysis (2016). http://geodesic.mathdoc.fr/item/DAS_2016_a10/