一维Witten Laplacian的再分析

一维Witten Laplacian算子的复活分析-- II

Resurgent analysis of the Witten Laplacian in one dimension -- II

本文用复苏分析的方法进一步研究了一维Witten Laplacian，以接近于WKB渐近性与圆盘瞬子的关系。本文提出了更精确的连接公式，它允许计算一个次优势指数项的超渐近展开的低的特征值。通过两个例子给出了对应于低本征值的本征函数的计算。

On Asymptotics and Resurgent Structures of Enumerative Gromov-Witten Invariants

Making use of large-order techniques in asymptotics and resurgent analysis, this work addresses the growth of enumerative Gromov-Witten invariants---in their dependence upon genus and degree of the embedded curve---for several different threefold Calabi-Yau varieties. In particular, while the leading asymptotics of these invariants at large genus or at large degree is exponential, at combined large genus and degree it turns out to be factorial. This factorial growth has a resurgent nature, originating via mirror symmetry from the resurgent-transseries description of the B-model free energy. Th…

从闭到相对高亏格 Gromov-Witten 不变量：通过复兴函数

From Closed to Relative Higher-Genus Gromov-Witten Invariants via Resurgent Functions

本文通过复兴函数研究已解锥形上高亏格 Gromov-Witten 不变量的强耦合展开，揭示其包含对偶变量闭曲线计数与相对不变量贡献。

相关衰减的Witten Laplacian方法

Witten Laplacian Methods for the Decay of Correlations

本文的目的是将直接方法应用于研究自然出现在统计力学和欧几里得场论中的积分。我们提供加权估计导致指数衰减的两点关联函数某些经典的凸无界模型。该方法涉及与系统的哈密顿量相关的Witten Laplacian方程的解的研究。

Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds

In this paper, for a Seifert loop (i.e., a knot in a Seifert three-manifold), first we give a family of an explicit function $Φ(q; N)$ whose special values at roots of unity are identified with the Witten-Reshetikhin-Turaev invariants of the Seifert loop for the integral homology sphere. Second, we show that the function $Φ(q; N)$ satisfies a $q$-difference equation whose classical limit coincides with a component of the character varieties of the Seifert loop. Third, we give an interpretation of the function $Φ(q; N)$ from the view point of the resurgent analysis.

关于Witten-Laplacian的谱性质、值域投影和Brascamp-Lieb不等式

On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality

研究了Helffer和Sj{<$}strand的一个积分恒等式，它对某类概率测度给出了两个函数（随机变量）的协方差公式。与Brascamp-Lieb不等式相比，该公式是分析统计力学中相关渐近性的一种更灵活、更强的方法。利用闭值域定理的一个精细形式，证明了该恒等式的有效性等价于欧氏空间上Witten-Laplacian的某些显式谱性质，并从所得到的值域投影的抽象表达式中推导出了该公式.作为推论，得到了Brascamp-Lieb不等式的推广形式.对于统计力学中的一类测度，从Repleson-Agmon公式、嵌入的紧性和伪微分算子的Weyl演算中得到了均值的显式判据，给出了闭值域、严格正性、本质自伴性和区域特征的结果.