Pith. sign in

REVIEW 2 cited by

Minimizers for an aggregation model with attractive-repulsive interaction

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2307.13769 v3 pith:GZV54VDM submitted 2023-07-25 math.AP math-phmath.CAmath.MPmath.OC

classification math.APmath-phmath.CAmath.MPmath.OC
keywords distancesinteractionminimizersshowingaggregationattractiveattractive-repulsivecertain
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Existence of minimizers for interaction energies with external potentials

    math.AP 2025-09 accept novelty 7.0 of 10

    For essentially convex interaction kernels, a threshold condition on an auxiliary density guarantees existence, uniqueness, and compact support of minimizers in R^d and curved half-spaces; a counterexample shows the t...

  2. A family of explicit minimizers for interaction energies

    math.AP 2025-01 accept novelty 7.0 of 10

    For odd dimensions with interaction powers (a,b)=(3,2-d) and even dimensions with (3,1-d), the unique energy minimizer is given explicitly, with d=1,2,3 in elementary functions.

Pith tools