Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters

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dc.contributor.authorKoohestani, Masoumeh
dc.contributor.authorObata, Nobuaki
dc.contributor.authorTanaka, Hajime
dc.date.accessioned2026-01-02T08:30:01Z
dc.date.issued2021
dc.description.abstractWe 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.
dc.description.sponsorshipThe 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.
dc.identifier.citationScaling 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
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2021.104
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 46L53; 60F05; 05E30
dc.identifier.otherarXiv:2106.14497
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211423
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleScaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2021, том 17, випуск за цей рік