珠粒过程的一种简化
A Finitization of the Bead Process
摘要：
珠过程是定义在平行线上的粒子系统，其基本度量为相邻线上的粒子交错的所有配置提供恒定权重，否则为零权重。基于$abc$ -六边形由三种菱形拼接的统计力学模型，定义了珠粒过程的有限化版本。相应的联合分布可以实现为随机矩阵序列的特征值密度函数。有限化bead过程是行列式的，我们用雅可比多项式给出了相关核。考虑两个缩放限制：一个全局限制，其中行之间的间距为零，和一定的批量缩放限制。在全局极限中，确定颗粒的支撑的形状，而在批量缩放极限中，在适当地识别其中的各向异性参数之后，回收Boutillier的珠处理内核。
英文摘要：
The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an $abc$-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices. The finitized bead process is determinantal, and we give the correlation kernel in terms of Jacobi polynomials. Two scaling limits are considered: a global limit in which the spacing between lines goes to zero, and a certain bulk scaling limit. In the global limit the shape of the support of the particles is determined, while in the bulk scaling limit the bead process kernel of Boutillier is reclaimed, after approriate identification of the anisotropy parameter therein.
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