The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters

• Date: 2018
• Main Authors: Grigorchuk, R. I., Krylyuk, Ya. S.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: group of intermediate growth; diatomic linear chain,random walk; spectral measure; Schreier graph; discrete Laplacian; 20F; 20P; 37A; 60J; 82D
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/703
• Journal Title: Algebra and Discrete Mathematics

It is shown that the KNS-spectral measure of the typical Schreier graph of the action of 3-generated 2-group of intermediate growth constructed by the first author in 1980 on the boundary of binary rooted tree  coincides with the Kesten’s spectral measure, and coincides (up to affine transformation...