论文标题
多核生长和Toda晶格
Polynuclear growth and the Toda lattice
论文作者
论文摘要
结果表明，多核生长模型是一个完全可以整合的马尔可夫过程，因为它的转变概率是由基于不变量测量的散射变换产生的核的弗雷德霍尔姆决定因素给出的，该测量值是绝对高度，连续的时间简单随机步行。从内核的线性演变来看，可以表明$ n $点分布是根据二维非亚洲Toda lattice演变而来的$ n \ times n $矩阵的决定因素。
It is shown that the polynuclear growth model is a completely integrable Markov process in the sense that its transition probabilities are given by Fredholm determinants of kernels produced by a scattering transform based on the invariant measures modulo the absolute height, continuous time simple random walks. From the linear evolution of the kernels, it is shown that the $n$-point distributions are determinants of $n\times n$ matrices evolving according to the two dimensional non-Abelian Toda lattice.
