A survey on zeros of random holomorphic sections
Turgay Bayraktar, Dan Coman, Hendrik Herrmann, George Marinescu
TL;DR
This survey reviews the distribution of zeros in random polynomials and holomorphic sections, highlighting recent results and introducing new measures supported on totally real subsets.
Contribution
It compiles existing knowledge on zeros distribution and presents new examples of measures supported on totally real subsets of the complex space.
Findings
Distribution patterns of zeros in random polynomials summarized.
New measures supported on totally real subsets introduced.
Insights into zeros of random holomorphic sections provided.
Abstract
We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some new examples of measures supported in totally real subsets of the complex probability space.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Meromorphic and Entire Functions