We give overcrowding estimates for the Sine(beta) process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having exactly n points in a fixed interval is given by e(-beta/2n2) log(n)+O(n(2)) as n -> infinity. We also identify the next order term in the exponent if the size of the interval goes to zero.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/625509 |
| Date | 08 1900 |
| Creators | Holcomb, Diane, Valkó, Benedek |
| Contributors | Univ Arizona, Dept Math |
| Publisher | INST MATHEMATICAL STATISTICS |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | Article |
| Rights | © Association des Publications de l’Institut Henri Poincaré, 2017 |
| Relation | http://projecteuclid.org/euclid.aihp/1500624035 |
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