The role of the density of states in Bose-Einstein condensation

The onset of Bose-Einstein condensation in systems with { various} densities of states is examined, with particular attention to the role of the behavior of their {energy} spectrum at low and high energies. Specifically, the results of Chatterjee and Diaconis, which rely exclusively on the high-energy behavior, are compared and reconciled with those of the standard physics approach, where the existence of condensation is determined by the low-energy behavior.