Non-Gaussian diffusion was recently observed in a gas mixture with mass and
fraction contrast [F. Nakai et al, Phys. Rev. E 107, 014605 (2023)]. The mean
square displacement of a minor gas particle with a small mass is linear in
time, while the displacement distribution deviates from the Gaussian
distribution, which is called the Brownian yet non-Gaussian diffusion. In this
work, we theoretically analyze this case where the mass contrast is
sufficiently large. Major heavy particles can be interpreted as immobile
obstacles, and a minor light particle behaves like a Lorentz gas particle
within an intermediate time scale. Despite the similarity between the gas
mixture and the conventional Lorentz gas system, the Lorentz gas description
cannot fully describe the Brownian yet non-Gaussian diffusion. A successful
description can be achieved through an ensemble average of the statistical
quantities of the Lorentz gas over the initial speed.