Large gap probabilities of complex and symplectic spherical ensembles with point charges
| Autor: | Byun, Sung-Soo, Park, Seongjae |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider $n$ eigenvalues of complex and symplectic induced spherical ensembles, which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the Riemann sphere under the insertion of point charges. For both cases, we show that the probability that there are no eigenvalues in a spherical cap around the poles has an asymptotic behaviour as $n\to \infty$ of the form $$ \exp\Big( c_1 n^2 + c_2 n\log n + c_3 n + c_4 \sqrt n + c_5 \log n + c_6 + \mathcal{O}(n^{-\frac1{12}}) \Big) $$ and determine the coefficients explicitly. Our results provide the second example of precise (up to and including the constant term) large gap asymptotic behaviours for two-dimensional point processes, following a recent breakthrough by Charlier. Comment: 42 pages, 5 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|