Tag: Riesz s-Energy
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Between Uniformity and Collision: A New Phase-Transition
A New Phase Transition for Energy-Minimal Point Distributions on the Interval Date: 2026-03-28 Author: Michael T. M. Emmerich There are at least two very natural ways to spread points on the unit interval . One can try to maximize the sum of all pairwise distances, or one can try to maximize the smallest pairwise distance.…
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The Hardness of Proving Hardness: Selecting Minimum Riesz Energy Subsets on a Line
Figure: Logarithmically scaled Riesz interaction matrix for a random set of 30 points on the unit interval, with cell sizes proportional to the distances between points. Each rectangle corresponds to a pair of points: darker cells indicate stronger interactions (points that are closer on the line), while lighter cells indicate weaker interactions. Off-diagonal entries show…
Michael Emmerich 