论文标题
二元根树的部分自动形态的光谱特性
Spectral properties of partial automorphisms of binary rooted tree
论文作者
论文摘要
我们研究了植根树的随机部分局部自动形态的光谱度量的渐近学。对于每个部分自动形态$ x $，我们分配其操作矩阵$ a_x $。结果表明，$ a_x $的特征值的均匀分布薄弱地收敛到$δ_0$，为$ n \ to \ infty $，其中$δ_0$是$ 0 $ $ 0 $的$δ_0$。
We study asymptotics of the spectral measure of a randomly chosen partial automorphism of a rooted tree. To every partial automorphism $x$ we assign its action matrix $A_x$. It is shown that the uniform distribution on eigenvalues of $A_x$ converges weakly in probability to $δ_0$ as $n \to \infty$, where $δ_0$ is the delta measure concentrated at $0$.
