Demonstrates continuity of bounded critical points of Riesz energy in 1D, suggesting new insights on kernel behavior.
In this paper we deal with the bounded critical points of a Riesz energy of attractive-repulsive type in dimension 1. Under suitable assumptions on the growth of the kernel in the origin, we are able to prove that they are continuous inside their support.
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Carazzato et al. (2026) studied this question.
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