Random zeros on complex manifolds: conditional expectations

Details Random zeros on complex manifolds: conditional expectations Random zeros on complex manifolds: conditional expectations

2010-05-23

arxiv.org/abs/1005.4166v1

Mathematics

Complex Variables

27 pages

Scientific paper

We study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The conditional distribution is analogous to the pair correlation function of zeros, but we show that it has quite a different small distance behavior. In particular, the conditional distribution does not exhibit repulsion of zeros in dimension one. To prove this, we give universal scaling asymptotics for the conditional zero distribution around p. The key tool is the conditional Szego kernel and its scaling asymptotics.

Affiliated with

Also associated with

No associations

Rating

Random zeros on complex manifolds: conditional expectations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random zeros on complex manifolds: conditional expectations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random zeros on complex manifolds: conditional expectations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-590512