The fact that Ω Ω ( E ) increases no faster than a power of the energy ensures that these moments will be finite. Therefore, we can expand the factor e − − β β E Ω Ω ( E ) about the mean value ⟨ ⟨ E ⟩ ⟩ , which will coincide with E ⋆ ⋆ for Gaussian fluctuations (i.e. average and most probable values coincide), and retaining lowest order terms result in