论文标题
有限尺寸校正与最长长度增加子序列的分布有关
Finite size corrections relating to distributions of the length of longest increasing subsequences
论文作者
论文摘要
考虑的是大的$ n $或大强度，即各种模型最长增加子序列的长度的分布形式。早期的工作已经确定，在居中和缩放之后，这些分布的极限定律与从随机矩阵理论已知的硬边的某些分布函数有关。通过分析难以软边的过渡，我们为Hammersley模型和对称性进行补充并扩展了Baik和Jenkins的结果，这使得领先的校正与$ Z^{ - 2/3} $成比例，其中$ Z^2 $是Poisson速率的强度，并根据范围衍生的形式衍生出限制法律的功能形式。我们的方法从弗雷德尔姆操作员理论量和潘勒维超越人方面赋予了功能形式。对于随机排列及其对称性，对精确的枚举和模拟的数值分析提供了令人信服的证据，表明领先的校正与$ n^{ - 1/3} $成正比，并且对其图形形式提供了近似值。
Considered are the large $N$, or large intensity, forms of the distribution of the length of the longest increasing subsequences for various models. Earlier work has established that after centring and scaling, the limit laws for these distributions relate to certain distribution functions at the hard edge known from random matrix theory. By analysing the hard to soft edge transition, we supplement and extend results of Baik and Jenkins for the Hammersley model and symmetrisations, which give that the leading correction is proportional to $z^{-2/3}$, where $z^2$ is the intensity of the Poisson rate, and provides a functional form as derivates of the limit law. Our methods give the functional form both in terms of Fredholm operator theoretic quantities, and in terms of Painlevé transcendents. For random permutations and their symmetrisations, numerical analysis of exact enumerations and simulations gives compelling evidence that the leading corrections are proportional to $N^{-1/3}$, and moreover provides an approximation to their graphical forms.
