Scaling limit of vicious walks and two-matrix model.
Scaling limit of vicious walks and two-matrix model.
复制标题
恶性游走和二矩阵模型的尺度限制。
DOI：
10.1103/physreve.66.011105
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
H. Tanemura
中科院分区：
文献类型：
--
作者：
M. Katori;H. Tanemura
考虑Fisher一维恶性步行者模型的扩散标度极限，导出了一个不相交的布朗运动系统。研究了N个粒子的空间分布，并用NxN高斯随机矩阵特征值的概率密度函数描述了N个粒子的空间分布。粒子分布取决于观测时间t与施加非相交条件的时间间隔t的比值。当t/ t从0到1时，会发生分布的转变，这与Pandey和Mehta的双矩阵模型中观察到的转变一致。尽管原始的恶性步行者模型中不存在矩阵结构，但在扩散尺度极限下，接触排斥相互作用的积累实现了多矩阵模型中特征值的相关分布作为粒子分布。
We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of N particles is studied and it is described by use of the probability density function of eigenvalues of NxN Gaussian random matrices. The particle distribution depends on the ratio of the observation time t and the time interval T in which the nonintersecting condition is imposed. As t/T is going on from 0 to 1, there occurs a transition of distribution, which is identified with the transition observed in the two-matrix model of Pandey and Mehta. Despite of the absence of matrix structure in the original vicious walker model, in the diffusion scaling limit, accumulation of contact repulsive interactions realizes the correlated distribution of eigenvalues in the multimatrix model as the particle distribution.