标题： 多个大区间的合流超几何核行列式 显示英文标题

标题： Confluent hypergeometric kernel determinant on multiple large intervals

摘要： 合流超几何点过程代表了一个普遍性类，它出现在多种不同但相关领域中。它特别描述了在广义酉系综的谱中间靠近Fisher-Hartwig奇点处特征值的局部统计特性。本文的目标是研究该过程在不相交区间集合$\cup_{j=0}^{n}(sa_j,sb_j)$上的大间隙渐近行为，其中$a_0<b_0<\dots<a_m<0<b_m<\dots<a_n<b_n$对于某些$0\leq m \leq n$。当$s\to +\infty$时，我们建立了一个一般渐近公式，包括阶数为$1$的振荡项，该公式涉及一个沿$n$维环面上线性流上的$\theta$-函数组合积分。如果线性流具有“良好的狄利克雷性质”或遍历性质，我们可以进一步改进积分渐近的误差估计或主项。 这些结果可以结合用于情况$n=1$，这导致了一个精确的大间隔渐近表达式，直到一个未确定的常数。 显示英文摘要

摘要： The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig singular point for a broad class of unitary ensembles. It is the aim of this work to investigate large gap asymptotics of this process over a union of disjoint intervals $\cup_{j=0}^{n}(sa_j,sb_j)$, where $a_0<b_0<\dots<a_m<0<b_m<\dots<a_n<b_n$ for some $0\leq m \leq n$. As $s\to +\infty$, we establish a general asymptotic formula up to and including the oscillatory term of order $1$, which involves a $\theta$-functions-combination integral along a linear flow on an $n$-dimensional torus. If the linear flow has ``good Diophantine properties'' or the ergodic properties, we further improve the error estimate or the leading term for the asymptotics of the integral. These results can be combined for the case $n=1$, which lead to a precise large gap asymptotics up to an undetermined constant.