多变量杂耍概率
Multivariate Juggling Probabilities
摘要：
我们考虑改进版本的马尔可夫链有关杂耍介绍沃灵顿。我们进一步推广的建设杂耍任意高度以及无限多个球，这是更简洁地表示在整数分区的马尔可夫链。在所有情况下，我们给出了明确的产品公式的平稳概率。在一种情况下，归一化因子可以明确地写为齐次对称多项式。我们还改进和推广了集划分上的丰富马尔可夫链。最后，我们证明了在一种情况下，平稳分布是在有界时间。
英文摘要：
We consider refined versions of Markov chains related to juggling introduced by Warrington. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in terms of Markov chains on integer partitions. In all cases, we give explicit product formulas for the stationary probabilities. The normalization factor in one case can be explicitly written as a homogeneous symmetric polynomial. We also refine and generalize enriched Markov chains on set partitions. Lastly, we prove that in one case, the stationary distribution is attained in bounded time.
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