Universality for conditional measures of the sine point process
| Autor: | Kuijlaars, Arno B. J., Miña-Díaz, Erwin |
|---|---|
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Journal of Approximation Theory 243 (2019), 1-24 |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $X \setminus I$. 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. Comment: 26 pages, no figures, revised version with Appendix B |
| Databáze: | arXiv |
| Externí odkaz: |
|