单面地图的Eigenvalue统计
Eigenvalue Statistics of One-Face Maps
摘要：
我们研究了表示单面映射的三个正则图的邻接矩阵。数值研究表明，这些矩阵的极限特征值统计是相同的那些更大的，更广泛的研究类随机矩阵理论。给出了亏格为零的映射的矩阵生成算法，并发现亏格为零的映射的特征值统计量与亏格为高的映射的特征值统计量有显著的不同。这些结果使我们推测，特征值统计依赖于刚性的基础地图，和缩放的特征值间距的分布从高斯正交包络的指数分布的地图大小增加相对于属。
英文摘要：
We examine the adjacency matrices of three-regular graphs representing one-face maps. Numerical studies reveal that the limiting eigenvalue statistics of these matrices are the same as those of much larger, and more widely studied classes from Random Matrix Theory. We present an algorithm for generating matrices corresponding to maps of genus zero, and find the eigenvalue statistics in the genus zero case differ strikingly from those of higher genus. These results lead us to conjecture that the eigenvalue statistics depend on the rigidity of the underlying map, and the distribution of scaled eigenvalue spacings shifts from that of the Gaussian Orthogonal Ensemble to the exponential distribution as the map size increases relative to the genus.
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