Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters
Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters
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DOI：
10.3842/sigma.2021.104
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
Masoumeh Koohestani;N. Obata;Hajime Tanaka
中科院分区：
文献类型：
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作者：
Masoumeh Koohestani;N. Obata;Hajime Tanaka
我们确定了关于吉布斯态的量子中心极限定理中可能的缩放极限，对于一个具有所谓的基不等于1的经典参数的不断增长的距离正则图。我们还明确地描述了邻接矩阵的归一化谱分布的相应弱极限。我们用已知的具有经典参数和无界直径的无限族距离正则图来证明我们的结果。
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.