论文标题
关于具有不均匀边缘的应急表的渐近枚举的简短说明
A Short Note on Asymptotic Enumeration of Contingency Tables with Non-Uniform Margins
论文作者
论文摘要
在此简短说明中，我们计算了具有不均匀边缘的应变表数量的精确渐近造型。更确切地说，对于参数$ n，δ，b，c> 0 $，我们考虑了第一个$ [n^δ] $行的矩阵集和列的第一个$ [n^Δ] $，其余的$ n $ lows and colums and columss and colums and cons and sum $ [cn] $。当使用Barvinok和Hartigan开发的最大熵方法时，我们计算该集合的基础性的精确渐近渐近学。本注释的唯一贡献是渐近公式中二次形式的决定因素的详细扩展。
In this short note, we compute the precise asymptotics for the number of contingency tables with non-uniform margins. More precisely, for parameter $n,δ, B,C>0$, we consider the set of matrices whose first $[n^δ]$ rows and columns have sum $[BCn]$ and the rest $n$ rows and columns have sum $[Cn]$. We compute the precise asymptotics of the cardinality of this set when $B<B_c=1+\sqrt{1+1/C}$ using the maximal entropy methods developed by Barvinok and Hartigan. The only contribution of this note is a detailed expansion of the determinant of quadratic forms in asymptotic formulas.
