论文标题
关于应急表和独立启发式的数量
On the number of contingency tables and the independence heuristic
论文作者
论文摘要
我们获得了$ N \ times n $应急表的敏锐渐近估计，其中有两个线性保证金$ cn $和$ bcn $。结果暗示了此类应急表数的二阶相变，其临界值为\ ts $ b_ {c}：= 1 + \ sqrt {1 + \ sqrt {1 + 1/c} $。结果，对于\ ts $ b> b> b_ {c} $，我们证明了经典\ emph {独立启发式}会导致大型秘密。
We obtain sharp asymptotic estimates on the number of $n \times n$ contingency tables with two linear margins $Cn$ and $BCn$. The results imply a second order phase transition on the number of such contingency tables, with a critical value at \ts $B_{c}:=1 + \sqrt{1+1/C}$. As a consequence, for \ts $B>B_{c}$, we prove that the classical \emph{independence heuristic} leads to a large undercounting.
