Spectral properties of partial automorphisms of a binary rooted tree

• Date: 2019
• Main Author: Kochubinska, Eugenia
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: partial automorphism; semigroup; eigenvalues; random matrix; delta measure; 20M18; 20M20,05C05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/532
• Journal Title: Algebra and Discrete Mathematics

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 \(\delta_0\) as \...