AI 中文总结
该研究针对离散多时间行列式点过程，证明其相关核在定义域限制下形式不变，将结果应用于两类填砌问题，发现其与可积核的特定方法存在显著类比。
AI 中文摘要
我们研究一类离散多时间行列式点过程，其相关核具有双轮廓积分形式，包含Schur过程作为简单例子。我们证明，当对该点过程限制定义域进行条件化时，相关核的形式保持不变，但被积函数会变得更复杂，且由黎曼-希尔伯特问题刻画。我们将该通用结果应用于缩小的Aztec钻石的多米诺骨牌填砌及带孔六边形的菱形填砌，结果显示其与可积核的Its-Izergin-Korepin-Slavnov方法存在显著类比。
英文摘要
We consider a class of discrete multi-time determinantal point processes whose correlation kernels admit a double-contour integral form, containing Schur processes as simple examples. We show that the form of the correlation kernel is preserved under conditioning of the point process to a restricted domain, however, with an integrand which becomes more complicated and which is characterized by a Riemann-Hilbert problem. We apply our general result to domino tilings of reduced Aztec diamonds and to lozenge tilings of hexagons with holes. Our results show a striking analogy with the Its-Izergin-Korepin-Slavnov method for integrable kernels.
Comments39 pages, 9 figures
