Gap metrics for stationary point processes and quantitative convexity of the free energy

In this article, we are interested in convexity properties of the free energy for stationary point processes on $\mathbb R$ w.r.t.\ a new geometry inspired by optimal transport. We will show for a rich class of pairwise interaction energies A) quantified strict convexity of the free energy implying uniqueness of minimizers B) existence of a gradient flow curve of the free energy w.r.t. the new metric converging exponentially fast to the unique minimizer. Examples for energies for which A holds include logarithmic or Riesz interactions with parameter $0<s<1$, examples for which A and B hold are hypersingular Riesz or Yukawa interactions.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-09-10

• Fields of study

  Mathematics

• Identifiers
  arXiv 2509.08659
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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