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A Periodic Long-Time Boltzmann--Grad Limit in Every Fixed Dimension $d\ge 4$ via Two-Landing-Root Packets
We prove a periodic long-time Boltzmann--Grad limit for hard spheres in every fixed spatial dimension $d\ge 4$. The componentwise long-bond estimate used in dimensions two and three does not yield the required arbitrary-dimensional power. Our replacement keeps two connected time sublayers as a singl
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