Bulk universality holds in measure for compactly supported measures
Let µ be a measure with compact support, with orthonormal polynomials { p n } and associated reproducing kernels { K n }. We show that bulk universality holds in measure in { ξ : µ′( ξ ) > 0}. More precisely, given ɛ, r > 0, the linear Lebesgue measure of the set { ξ : µ′( ξ ) > 0} and for...
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| Veröffentlicht in: | Journal d'analyse mathématique (Jerusalem) 2012, Vol.116 (1), p.219-253 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let µ be a measure with compact support, with orthonormal polynomials {
p
n
} and associated reproducing kernels {
K
n
}. We show that bulk universality holds in measure in {
ξ
: µ′(
ξ
) > 0}. More precisely, given
ɛ, r
> 0, the linear Lebesgue measure of the set {
ξ
: µ′(
ξ
) > 0} and for which
approaches 0 as
n
→ ∞. There are no local or global regularity conditions on the measure µ. |
|---|---|
| ISSN: | 0021-7670 1565-8538 |
| DOI: | 10.1007/s11854-012-0006-6 |