有穷级渐近体制的起始点
Onset of the Asymptotic Regime for Finite Orders
摘要：
我们描述了一个马尔可夫链蒙特卡罗算法，它可以用来产生自然标记的n元偏序集在随机的概率分布的一个人的选择。实现这种算法的均匀分布，我们探索的方法，几乎每一个偏序集采取的三层结构描述的Kleitman和Rothschild（KR）的渐近制度。通过跟踪几个顺序不变量的n-依赖，其中的偏序集的高度，我们观察到的振荡行为，这是非常不同的单调方法KR政权。只有在n=40左右，这种“有限大小的舞蹈”才会逐渐过渡到渐近状态，直到n=85，这是我们模拟的最大n。
英文摘要：
We describe a Markov-Chain-Monte-Carlo algorithm which can be used to generate naturally labeled n-element posets at random with a probability distribution of one's choice. Implementing this algorithm for the uniform distribution, we explore the approach to the asymptotic regime in which almost every poset takes on the three-layer structure described by Kleitman and Rothschild (KR). By tracking the n-dependence of several order-invariants, among them the height of the poset, we observe an oscillatory behavior which is very unlike a monotonic approach to the KR regime. Only around n=40 or so does this "finite size dance" appear to give way to a gradual crossover to asymptopia which lasts until n=85, the largest n we have simulated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
