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 -