论文标题
随机平面分区的大部分：泊松限制定理
Large Parts of Random Plane Partitions: a Poisson Limit Theorem
论文作者
论文摘要
我们提出了与尺寸超过某个适当选择水平的零件计数相关的平面分区统计渐近分析统计渐近分析的侵犯。在我们的研究中，我们使用了1973年斯坦利（Stanley）在1973年引入的正整数$ n $平面分区的共轭痕迹的概念。我们使用基于鞍点方法的一般方案来得出生成功能，并确定大部分计数的渐近行为。通过这种方式，我们可以证明泊松限制定理，用于$ n $的随机且均匀选择的平面分区的零件数量，其大小大于函数$ m = m（n）$作为$ n \ to \ infty $。还给出了$ m（n）$的明确表达式。
We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the positive integer $n$, introduced by Stanley in 1973. We derive generating functions and determine the asymptotic behavior of counts of large parts using a general scheme based on the saddle point method. In this way, we are able to prove a Poisson limit theorem for the number of parts of a random and uniformly chosen plane partition of $n$, whose sizes are greater than a function $m=m(n)$ as $n\to\infty$. An explicit expression for $m(n)$ is also given.
