Lorentz gas with small scatterers

The paper proves exactly the joint-limit nonstandard CLT the model asserted was likely still open. Theorem A states that for the planar periodic Lorentz gas with circular scatterers of radius ρ, along any joint limit with n→∞ and ρ→0 satisfying M(ρ)=o(log n), one has κ_{n,ρ}/b_{n,ρ} ⇒ N(0,Σ) with b_{n,ρ}=√(n log(n/ρ^2))/√(4πρ) and Σ=(1/π)I2 . The precise form of M(ρ) is given in Theorem 7.1, namely M(ρ)=max{Cργρ^{-2}, Ĉργ̂ρ^{-2}}+Cρ^{-2}, derived via spectral perturbation of transfer operators (Nagaev–Guivarc’h method on anisotropic Banach spaces), not via Young towers, and this yields the limiting characteristic function using the eigenvalue expansion (Proposition 6.3) . The authors also obtain a local limit theorem and mixing in the same joint regime . They explicitly frame their result as answering the joint-limit problem highlighted as open by Marklof–Tóth (2016), thereby filling the intermediate regime between the previously known one-parameter limits .