竞争骨灰盒的条件负关联
Conditional negative association for competing urns
摘要：
竞争骨灰盒是指随机试验，其中m个球随机且独立地落入骨灰盒1，.，n.形式上，我们有一个随机映射$σ$，来自{1，.，m}到{1，.，n}与$σ(i)$的i.i.d.与$x_j$的事件，至少$t_j$球降落在瓮j（对于一些阈值$t_j$）的指标，我们证明了条件负关联的随机变量$x_1,...,x_n$。我们主要处理更一般的情况下，$σ(i)$的不需要同分布，证明结果意味着条件负关联的独立同分布。案子一些结果-特别是引理8图方向-被认为是独立的利益。我们还给出了D的一个负相关猜想的一个反例. Welsh是G.法尔
英文摘要：
Competing urns refers to the random experiment where m balls are dropped, randomly and independently, into urns 1,...,n. Formally, we have a random map $σ$ from {1,...,m} to {1,...,n} with the $σ(i)$'s i.i.d. With $x_j$ the indicator of the event that at least $t_j$ balls land in urn j (for some threshold $t_j$), we prove conditional negative association for the random variables $x_1,...,x_n$. We mostly deal with the more general situation in which the $σ(i)$'s need not be identically distributed, proving results which imply conditional negative association in the i.i.d. case. Some of the results--particularly Lemma 8 on graph orientations--are thought to be of independent interest. We also give a counterexample to a negative correlation conjecture of D. Welsh, a strong version of a (still open) conjecture of G. Farr.
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