arXiv Open Access 2011

Scaled Correlations of Critical Points of Random Sections on Riemann Surfaces

John Baber

Lihat Sumber

Abstrak

In this paper we prove that as N goes to infinity, the scaling limit of the correlation between critical points z1 and z2 of random holomorphic sections of the N-th power of a positive line bundle over a compact Riemann surface tends to 2/(3pi^2) for small sqrt(N)|z1-z2|. The scaling limit is directly calculated using a general form of the Kac-Rice formula and formulas and theorems of Pavel Bleher, Bernard Shiffman, and Steve Zelditch.

Topik & Kata Kunci

math.CV

Penulis (1)

John Baber

Format Sitasi

APA MLA BibTeX

Baber, J. (2011). Scaled Correlations of Critical Points of Random Sections on Riemann Surfaces. https://arxiv.org/abs/1106.4737

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2011
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓