Universality for conditional measures of the sine point process

The sine process is a rigid point process on the real line, which means that for almost all configurations X, the number of points in an interval I=[−R,R] is determined by the points of X outside of I. In addition, the points in I are an orthogonal polynomial ensemble on I with a weight function tha...

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Bibliographic Details
Published in:Journal of approximation theory 2019-07, Vol.243, p.1-24
Main Authors: Kuijlaars, Arno B.J., Miña-Díaz, Erwin
Format: Article
Language:English
Subjects:
Conditional measures
Determinantal point processes
Orthogonal polynomials
Sine kernel
Universality limits
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Summary:The sine process is a rigid point process on the real line, which means that for almost all configurations X, the number of points in an interval I=[−R,R] is determined by the points of X outside of I. In addition, the points in I are an orthogonal polynomial ensemble on I with a weight function that is determined by the points in X∖I. We prove a universality result that in particular implies that the correlation kernel of the orthogonal polynomial ensemble tends to the sine kernel as the length |I|=2R tends to infinity, thereby answering a question posed by A.I. Bufetov.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2019.03.002