Random Matrix Theory with an External Source

Edouard Brézin, Shinobu Hikami (Autoren)

Buch | Softcover

138 Seiten

2017 | 1st ed. 2016
Springer Verlag, Singapore
978-981-10-3315-5 (ISBN)

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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.

Erscheinungsdatum	08.03.2017
Reihe/Serie	SpringerBriefs in Mathematical Physics ; 19
Reihe/Serie	SpringerBriefs in Mathematical Physics ; 19
Zusatzinfo	XII, 138 p.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	2D quantum gravity • Gaussian random matrix models • Gromov-Witten invariants • Kontsevich Airy matrix model • Random Matrix Theory
ISBN-10	981-10-3315-3 / 9811033153
ISBN-13	978-981-10-3315-5 / 9789811033155
Zustand	Neuware