The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters
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...
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| Видавець: | Lugansk National Taras Shevchenko University |
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| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/703 |
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Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-703 |
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oai:ojs.admjournal.luguniv.edu.ua:article-7032018-04-04T09:53:26Z The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters Grigorchuk, R. I. Krylyuk, Ya. S. group of intermediate growth, diatomic linear chain,random walk, spectral measure, Schreier graph, discrete Laplacian 20F, 20P, 37A, 60J, 82D 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 of \(\mathbb R\)) with the density of states of the corresponding diatomic linear chain. Jacoby matrix associated with Markov operator of simple random walk on these graphs is computed. It shown shown that KNS and Kesten's spectral measures of the Schreier graph based on the orbit of the point \(1^{\infty}\) are different but have the same support and are absolutely continuous with respect to the Lebesgue measure. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/703 Algebra and Discrete Mathematics; Vol 13, No 2 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/703/236 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
group of intermediate growth diatomic linear chain,random walk spectral measure Schreier graph discrete Laplacian 20F 20P 37A 60J 82D |
| spellingShingle |
group of intermediate growth diatomic linear chain,random walk spectral measure Schreier graph discrete Laplacian 20F 20P 37A 60J 82D Grigorchuk, R. I. Krylyuk, Ya. S. The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters |
| topic_facet |
group of intermediate growth diatomic linear chain,random walk spectral measure Schreier graph discrete Laplacian 20F 20P 37A 60J 82D |
| format |
Article |
| author |
Grigorchuk, R. I. Krylyuk, Ya. S. |
| author_facet |
Grigorchuk, R. I. Krylyuk, Ya. S. |
| author_sort |
Grigorchuk, R. I. |
| title |
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters |
| title_short |
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters |
| title_full |
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters |
| title_fullStr |
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters |
| title_full_unstemmed |
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters |
| title_sort |
spectral measure of the markov operator related to 3-generated 2-group of intermediate growth and its jacobi parameters |
| description |
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 of \(\mathbb R\)) with the density of states of the corresponding diatomic linear chain. Jacoby matrix associated with Markov operator of simple random walk on these graphs is computed. It shown shown that KNS and Kesten's spectral measures of the Schreier graph based on the orbit of the point \(1^{\infty}\) are different but have the same support and are absolutely continuous with respect to the Lebesgue measure. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/703 |
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2024-04-12T06:27:28Z |
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2024-04-12T06:27:28Z |
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