黎曼曲面上随机截面临界点的标度相关性
复变函数
2015-05-28 v4
摘要
本文证明，当 N 趋于无穷时，紧黎曼曲面上正线丛的 N 次幂的随机全纯截面的临界点 z1 和 z2 之间的相关性，在 sqrt(N)|z1-z2| 较小时的标度极限趋于 2/(3π^2)。该标度极限是使用 Kac-Rice 公式的一般形式以及 Pavel Bleher、Bernard Shiffman 和 Steve Zelditch 的公式与定理直接计算得出的。
引用
@article{arxiv.1106.4737,
title = {Scaled Correlations of Critical Points of Random Sections on Riemann Surfaces},
author = {John Baber},
journal= {arXiv preprint arXiv:1106.4737},
year = {2015}
}
备注
55 pages. LaTeX. output.txt is the output of running heisenberg_simpler.mpl through maple. heisenberg_simpler.mpl can be run by maple at the command line by saying 'maple -q heisenberg_simpler.mpl' to see the maple calculations that generated the matrices U(t) and D(t) described in the paper's appendix. It may also be run by opening it with GUI maple