For infinite-horizon Lorentz gas and stadium channel, the spreading density is a Lambert-corrected Gaussian core with power-law corridor tails; the renewal Lévy walk works for the Lorentz gas but not for the stadium channel.
Therefore we find forn = 1 (I) π 4− sin−1 (√ 2R ) ≤β≤ cos−1(2R), (i) cos(β)− sin(β)−R≤b≤R, (D8) and (II) cos−1(2R)≤β≤ π 4, (ii) R− sin(β)≤b≤ cos(β)−R
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Infinite horizon billiards: Transport at the border between Gauss and L\'evy universality classes
For infinite-horizon Lorentz gas and stadium channel, the spreading density is a Lambert-corrected Gaussian core with power-law corridor tails; the renewal Lévy walk works for the Lorentz gas but not for the stadium channel.