Non-colliding billiards in the plane
Itai Benjamini; Alexander Shamov; Barak Weiss · 2026 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
The study found no significant effect — useful as a negative control or null benchmark for your own design.
Abstract (excerpt)
We present an open problem about non-colliding freely moving hard disks in the Euclidean plane, together with related positive and negative partial results. The open problem is stated in a non-degenerate form: velocities are required to be pairwise distinct and their speeds are required to be uniformly bounded away from infinity. The positive deterministic result gives a bounded, injective, non-colliding velocity assignment for the integer lattice; after a common velocity shift, the speeds are also bounded away from zero. The negative result shows that no bounded continuous vector field on the
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Metadata source: arXiv