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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2012 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152209 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862579599935799296 |
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| author | Grigorchuk, R.I. Krylyuk, Ya.S. |
| author_facet | Grigorchuk, R.I. Krylyuk, Ya.S. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-26T19:17:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152209 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T19:17:02Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Grigorchuk, R.I. Krylyuk, Ya.S. 2019-06-08T18:26:46Z 2019-06-08T18:26:46Z 2012 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. https://nasplib.isofts.kiev.ua/handle/123456789/152209 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. The first author is supported by NSF grants DMS-0456185 and DMS-06000975. Both authors are supported by Max-Planck Institut of Mathematiks, Bonn. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters Article published earlier |
| spellingShingle | 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. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152209 |
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