论文标题
muttalib-硼丁素平面分区和随机矩阵合奏的硬边缘
Muttalib--Borodin plane partitions and the hard edge of random matrix ensembles
论文作者
论文摘要
我们研究了自然体积加权平面分区及其连续类似物的概率和组合方面。我们证明，在随机矩阵理论的新的和已知的硬质和软边分布方面，这些集团最大的部分渐近极限定律。作为推论，我们获得了Gumbel和Tracy之间的渐近跃迁 - 该平面分区最大部分的WIDOM GUE波动波动，连续的Bessel内核提供了插值。我们用两个定向上一段渗透的自然模型（LPP）来解释我们的结果：一种离散的$（\ max， +）$ infinite-nite-Geometry模型，具有快速衰减的几何体重，以及连续的$（\ min，\ cdot）$模型。
We study probabilistic and combinatorial aspects of natural volume-and-trace weighted plane partitions and their continuous analogues. We prove asymptotic limit laws for the largest parts of these ensembles in terms of new and known hard- and soft-edge distributions of random matrix theory. As a corollary we obtain an asymptotic transition between Gumbel and Tracy--Widom GUE fluctuations for the largest part of such plane partitions, with the continuous Bessel kernel providing the interpolation. We interpret our results in terms of two natural models of directed last passage percolation (LPP): a discrete $(\max, +)$ infinite-geometry model with rapidly decaying geometric weights, and a continuous $(\min, \cdot)$ model with power weights.
