Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters
We determine the possible scaling limits in the quantum central limit theorem with respect to the Gibbs state, for a growing distance-regular graph that has so-called classical parameters with base unequal to one. We also describe the corresponding weak limits of the normalized spectral distribution...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211423 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters. Masoumeh Koohestani, Nobuaki Obata and Hajime Tanaka. SIGMA 17 (2021), 104, 22 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862614155561795584 |
|---|---|
| author | Koohestani, Masoumeh Obata, Nobuaki Tanaka, Hajime |
| author_facet | Koohestani, Masoumeh Obata, Nobuaki Tanaka, Hajime |
| citation_txt | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters. Masoumeh Koohestani, Nobuaki Obata and Hajime Tanaka. SIGMA 17 (2021), 104, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We determine the possible scaling limits in the quantum central limit theorem with respect to the Gibbs state, for a growing distance-regular graph that has so-called classical parameters with base unequal to one. We also describe the corresponding weak limits of the normalized spectral distribution of the adjacency matrix explicitly. We demonstrate our results with the known infinite families of distance-regular graphs having classical parameters and with unbounded diameter.
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| first_indexed | 2026-03-14T08:19:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211423 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T08:19:48Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Koohestani, Masoumeh Obata, Nobuaki Tanaka, Hajime 2026-01-02T08:30:01Z 2021 Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters. Masoumeh Koohestani, Nobuaki Obata and Hajime Tanaka. SIGMA 17 (2021), 104, 22 pages 1815-0659 2020 Mathematics Subject Classification: 46L53; 60F05; 05E30 arXiv:2106.14497 https://nasplib.isofts.kiev.ua/handle/123456789/211423 https://doi.org/10.3842/SIGMA.2021.104 We determine the possible scaling limits in the quantum central limit theorem with respect to the Gibbs state, for a growing distance-regular graph that has so-called classical parameters with base unequal to one. We also describe the corresponding weak limits of the normalized spectral distribution of the adjacency matrix explicitly. We demonstrate our results with the known infinite families of distance-regular graphs having classical parameters and with unbounded diameter. The authors thank the anonymous referees for their valuable comments. HT thanks Professor Tom Koornwinder for letting him know that the measure µ∞ with γ = 0 in Section 6.1 corresponds to the Al-Salam–Chihara polynomials, and for providing relevant references. Part of this work was done while MK was visiting Tohoku University from February to July 2020, supported by K.N. Toosi University of Technology, Office of Vice-Chancellor for Global Strategies and International Affairs. NO and HT were supported by JSPS KAKENHI Grant Number JP19H01789. HT was also supported by JSPS KAKENHI Grant Numbers JP17K05156 and JP20K03551. This work was also partially supported by the Research Institute for Mathematical Sciences at Kyoto University. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters Article published earlier |
| spellingShingle | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters Koohestani, Masoumeh Obata, Nobuaki Tanaka, Hajime |
| title | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters |
| title_full | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters |
| title_fullStr | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters |
| title_full_unstemmed | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters |
| title_short | Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters |
| title_sort | scaling limits for the gibbs states on distance-regular graphs with classical parameters |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211423 |
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