TY - JOUR

T1 - Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters

AU - Koohestani, Masoumeh

AU - Obata, Nobuaki

AU - Tanaka, Hajime

N1 - Funding Information:
The authors thank the anonymous referees for 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.
Publisher Copyright:
© 2021, Institute of Mathematics. All rights reserved.

PY - 2021

Y1 - 2021

N2 - 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 explicitly the corresponding weak limits of the normalized spectral distribution of the adjacency matrix. We demonstrate our results with the known infinite families of distance-regular graphs having classical parameters and with unbounded diameter.

AB - 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 explicitly the corresponding weak limits of the normalized spectral distribution of the adjacency matrix. We demonstrate our results with the known infinite families of distance-regular graphs having classical parameters and with unbounded diameter.

KW - Classical parameters

KW - Distance-regular graph

KW - Gibbs state

KW - Quantum central limit theorem

KW - Quantum probability

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U2 - 10.3842/SIGMA.2021.104

DO - 10.3842/SIGMA.2021.104

M3 - Article

AN - SCOPUS:85122282195

SN - 1815-0659

VL - 17

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 104

ER -