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We determine the possible scaling limits in the quantum central limit theoremwith respect to the Gibbs state, for a growing distance-regular graph that hasso-called classical parameters with base unequal to one. We also describeexplicitly the corresponding weak limits of the normalized spectraldistribution of the adjacency matrix. We demonstrate our results with the knowninfinite families of distance-regular graphs having classical parameters andwith unbounded diameter.

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