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SpringerBriefs in Mathematical Physics

Random Matrix Theory with an External Source

Authors: Brézin, Edouard, Hikami, Shinobu

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  • 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 external source
  • Obtains the topological invariants such as the intersection numbers of the moduli space of spin curves by the duality and replica method in the scaling limit of the external source
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eBook $54.99
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  • ISBN 978-981-10-3316-2
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Softcover $69.99
price for USA in USD
  • ISBN 978-981-10-3315-5
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About this book

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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-981-10-3316-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-981-10-3315-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Random Matrix Theory with an External Source
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
19
Copyright
2016
Publisher
Springer Singapore
Copyright Holder
The Author(s)
eBook ISBN
978-981-10-3316-2
DOI
10.1007/978-981-10-3316-2
Softcover ISBN
978-981-10-3315-5
Series ISSN
2197-1757
Edition Number
1
Number of Pages
XII, 138
Topics