We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean spaces, and show that there are subsequences of radii for which the number variance grows at least as fast as the volume of the boundary of Euclidean balls, generalizing a classical result of Beck.
Reference: M. Björklund, M. Byléhn, "Hyperuniformity of random measures on Euclidean and hyperbolic spaces". Preprint.