From Random Polynomials to Symplectic Geometry

Details From Random Polynomials to Symplectic Geometry From Random Polynomials to Symplectic Geometry

2000-10-10

arxiv.org/abs/math-ph/0010012v1

Physics

Mathematical Physics

Expository article for Proceedings ICMP 2000

Scientific paper

We review some recent results on random polynomials and their generalizations
in complex and symplectic geometry. The main theme is the universality of
statistics of zeros and critical points of (generalized) polynomials of degree
$N$ on length scales of order $\frac{D}{\sqrt{N}}$ (complex case), resp.
$\frac{D}{N}$ (real case).

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