<div class="csl-bib-body">
<div class="csl-entry">Eichinger, B. (2023, September 8). <i>Necessary and sufficient conditions for Universality Limits</i> [Conference Presentation]. Pure Mathematics Seminar, Lancaster, United Kingdom of Great Britain and Northern Ireland (the).</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/189453
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dc.description.abstract
In this talk I present necessary and sufficient conditions for universality limits for orthog onal polynomials on the real line. One of our results is that the Christoffel–Darboux kernel has sine kernel asymptotics at a point ξ, with regularly varying scaling, if and only if the orthogonality measure (spectral measure) has a unique tangent measure at ξ and that is the Lebesgue measure. This includes all prior results with absolutely continuous or singular measures. In fact, sine kernel asymptotics is a special case of a more general theory which also includes hard edge universality limits; we show that the Christoffel–Darboux kernel has a regularly varying scaling limit if and only if the orthogonality measure has a unique tangent measure at ξ and that is not the point mass at ξ. In this case the limit kernel is expressible in terms of confluent hypergeometric functions. This talk is based on a joint work in progress with Milivoje Lukic and Harald Woracek.
en
dc.language.iso
en
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dc.subject
universality limits
en
dc.subject
orthogonal polynomials
en
dc.subject
canonical systems
en
dc.title
Necessary and sufficient conditions for Universality Limits
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Conference Presentation
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E101-01 - Forschungsbereich Analysis
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tuw.event.name
Pure Mathematics Seminar
en
tuw.event.startdate
08-09-2023
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tuw.event.enddate
08-09-2023
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Lancaster
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tuw.event.country
GB
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tuw.event.institution
Lancaster University, UK
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tuw.event.presenter
Eichinger, Benjamin
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
conference paper not in proceedings
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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crisitem.author.dept
E101-01 - Forschungsbereich Analysis
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crisitem.author.parentorg
E101 - Institut für Analysis und Scientific Computing
