复射影空间上随机全纯截面临界点的期望个数

作为随机全纯截面范数集的Fekete点

Fekete Points as Norming Sets for Random Holomorphic Sections

该研究证明紧Kähler流形上正Hermitian线丛的Fekete构型是随机全纯截面的渐近精确范数集，还给出相关范数比较与收敛结论，构造了反例并推导了相关条件。

随机全纯截面零点渐近平衡分布综述

A survey on asymptotic equilibrium distribution of zeros of random holomorphic sections

综述随机全纯多项式与正线丛高次幂全纯截面零点渐近平衡分布，重点阐述多复变势理论的作用。

A survey on zeros of random holomorphic sections

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.

辛流形上几乎全纯截面的渐近性

Asymptotics of almost holomorphic sections on symplectic manifolds

研究了几乎复辛流形上的样本线丛$L \to M$的几乎全纯截面$s \in H^0_J(M, ω)$在Boutet de Monvel-Guillemin意义下的渐近性.这样的截面被定义为一个复形的核，该复形类似于复流形上的正线丛的$\bar{\partial}$复形。我们的主要结果是Szego投影机$Π_N$的幂$L^N$的标度极限渐近性。Kodaira嵌入定理和Tian几乎等距定理几乎是标度极限的直接结果。我们也将这种几乎全纯部分的渐近全纯部分的意义上的唐纳森和Auroux。

Large deviations for zeros of holomorphic sections on punctured Riemann surfaces

In this article we obtain large deviation estimates for zeros of random holomorphic sections on punctured Riemann surfaces. These estimates are then employed to yield estimates for the respective hole probabilities. A particular case of relevance that is covered by our setting is that of cusp forms on arithmetic surfaces. Most of the results we obtain also allow for reasonably general probability distributions on holomorphic sections, which shows the universal character of these estimates. Finally, we also extend our results to the case of certain higher dimensional complete Hermitian manifold…

非紧复流形上随机全纯截面因子的渐近正态性

Asymptotic Normality of Divisors of Random Holomorphic Sections on Non-compact Complex Manifolds

本文研究非紧 Hermite 流形上随机全纯截面零因子的统计行为，证明相关光滑线性统计量满足中心极限定理。