THE SIZE OF THE LARGEST PART OF RANDOM PLANE PARTITIONS OF LARGE INTEGERS
THE SIZE OF THE LARGEST PART OF RANDOM PLANE PARTITIONS OF LARGE INTEGERS
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大整数随机平面分部最大部分的大小
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Ljuben S. Mutafchiev
中科院分区：
文献类型：
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作者：
Ljuben S. Mutafchiev
研究了正整数n的平面分拆ω的最大部分尺寸的渐近性质，假设ω是从所有这样的分拆的集合中随机一致选取的.我们证明了这个特征，适当地归一化，当n → ∞时，弱倾向于具有极值概率分布的随机变量，分布函数等于e-e-z，−∞ < z < ∞。将平面划分表示为立体图表明，对于n的随机平面划分的行数和列数，同样的极限定理也成立。
We study the asymptotic behavior of the largest part size of a plane partition ω of the positive integer n, assuming that ω is chosen uniformly at random from the set of all such partitions. We prove that this characteristic, appropriately normalized, tends weakly, as n → ∞, to a random variable having an extreme value probability distribution with distribution function, equal to e−e −z ,−∞ < z < ∞. The representation of a plane partition as a solid diagram shows that the same limit theorem holds for the numbers of rows and columns of a random plane partition of n.