| 书目名称 | Random Matrix Theory with an External Source |
| 编辑 | Edouard Brézin,Shinobu Hikami |
| 视频video | |
| 概述 | Expresses the correlation function of the Gaussian random matrix model with an external source in the integral formula.Examines universal behaviors of level spacing distributions for an arbitrary exte |
| 丛书名称 | SpringerBriefs in Mathematical Physics |
| 图书封面 |  |
| 描述 | This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.. |
| 出版日期 | Book 2016 |
| 关键词 | Random matrix theory; Gaussian random matrix models; 2D quantum gravity; Kontsevich Airy matrix model; G |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-981-10-3316-2 |
| isbn_softcover | 978-981-10-3315-5 |
| isbn_ebook | 978-981-10-3316-2Series ISSN 2197-1757 Series E-ISSN 2197-1765 |
| issn_series | 2197-1757 |
| copyright | The Author(s) 2016 |
发表于 2025-3-21 17:51:19
