تقرير
On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities
| العنوان: | On the Fredholm determinant of the confluent hypergeometric kernel with discontinuities |
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| المؤلفون: | Xu, Shuai-Xia, Zhao, Shu-Quan, Zhao, Yu-Qiu |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics |
| الوصف: | We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near the Fisher-Hartwig singularity. Applying the Riemann-Hilbert method, we study the generating function of this process on any given number of intervals. It can be expressed as the Fredholm determinant of the confluent hypergeometric kernel with $n$ discontinuities. In this paper, we derive an integral representation for the determinant by using the Hamiltonian of the coupled Painlev\'e V system. By evaluating the total integral of the Hamiltonian, we obtain the asymptotics of the determinant as the $n$ discontinuities tend to infinity up to and including the constant term. Here the constant term is expressed in terms of the Barnes $G$-function. Comment: 36 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.11214 |
| رقم الأكسشن: | edsarx.2402.11214 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |