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...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2021
Автори: Koohestani, Masoumeh, Obata, Nobuaki, Tanaka, Hajime
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2021
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211423
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
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.
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
work_keys_str_mv AT koohestanimasoumeh scalinglimitsforthegibbsstatesondistanceregulargraphswithclassicalparameters
AT obatanobuaki scalinglimitsforthegibbsstatesondistanceregulargraphswithclassicalparameters
AT tanakahajime scalinglimitsforthegibbsstatesondistanceregulargraphswithclassicalparameters