Second-order velocity structure function for the velocity field outside the AGN-dominant region (≳60 kpc) in Perseus, grouped into four bins (red points). Black points show all available velocity pairs with their 1σ statistical uncertainties. The shaded regions show theoretical predictions and their 68% scatters based on Gaussian random fields. Various energy injection scales (top) and spectral indices are shown to compare with the observations. The XRISM Perseus dataset favors a large injection scale (at least a few hundred kpc) but is not sensitive to the spectral index (see Sect. 4.2).