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 o...
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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152209 |
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| Цитувати: | The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters / R.I. Grigorchuk, Ya.S. Krylyuk // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 2. — С. 237–272. — Бібліогр.: 39 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152209 |
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dspace |
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irk-123456789-1522092019-06-09T01:25:18Z 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. 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 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∞ are different but have the same support and are absolutely continuous with respect to the Lebesgue measure. 2012 Article The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters / R.I. Grigorchuk, Ya.S. Krylyuk // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 2. — С. 237–272. — Бібліогр.: 39 назв. — англ. 1726-3255 2010 MSC:20F, 20P, 37A, 60J, 82D. http://dspace.nbuv.gov.ua/handle/123456789/152209 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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 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∞ are different but have the same support and are absolutely continuous with respect to the Lebesgue measure. |
| format |
Article |
| author |
Grigorchuk, R.I. Krylyuk, Ya.S. |
| spellingShingle |
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 Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152209 |
| citation_txt |
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters / R.I. Grigorchuk, Ya.S. Krylyuk // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 2. — С. 237–272. — Бібліогр.: 39 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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