For d≥4 and small mirror density p, the Lorentz mirror walk has second moment (2d-1)/(d-1) T/p within error p^{1/9} for all T up to exp(log^2(1/p)).
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Diffusivity of the Lorentz mirror walk in high dimensions
For d≥4 and small mirror density p, the Lorentz mirror walk has second moment (2d-1)/(d-1) T/p within error p^{1/9} for all T up to exp(log^2(1/p)).