论文标题
二进制偶然表的渐近枚举以及与独立启发式的比较
Asymptotic Enumeration of Binary Contingency Tables and Comparison with Independence Heuristic
论文作者
论文摘要
对于参数，$ n，δ，b，c $，我们获得了$（n+\ lfloor n^δ\ rfloor）数量的尖锐渐近公式，^2 $ - 维二进制二进制二进制表，不均匀的边缘，具有$ \ lfloor bcn bcn \ rfloor $ $ $ \ lfor $ cn的不均匀边缘。此外，我们比较了我们的敏锐渐近物质与经典的独立性启发式估计，并证明独立性启发式高估了$ e^{θ（n^{2Δ}}} $的倍数。我们的比较是基于对相关比的分析，并且还获得了$θ$的常数的显式结合。
For parameters $n,δ,B,C$, we obtained a sharp asymptotic formula for the number of $(n+\lfloor n^δ\rfloor)^2$-dimensional binary contingency tables with non-uniform margins taking values of $\lfloor BCn\rfloor$ and $\lfloor Cn\rfloor$. Furthermore, we compared our sharp asymptotics with the classical independence heuristic estimate and proved that the independence heuristic overestimates by a factor of $e^{Θ(n^{2δ})}$. Our comparison is based on the analysis of the correlation ratio and an explicit bound for the constant in $Θ$ is also obtained.
