EAN: 9789811033155

RANDOM MATRIX THEORY WITH AN EXTERNAL SOURCE - ...

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.

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