We study properties of eigenvalues of a matrix associated with a randomly chosen partial automorphism of a regular rooted tree. We show that asymptotically, as the level number goes to infinity, the fraction of non-zero eigenvalues converges to zero in probability.

中文翻译：

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正则有根树的部分自同构谱

我们研究与随机选择的规则有根树的部分自同构相关的矩阵的特征值的性质。我们逐渐证明，随着级别数趋于无穷大，非零特征值的分数在概率上收敛到零。