We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely continuous with an unbounded density, thereby settling a question that was left open in previous works.
Properties of probability measures on the set of quantum states and their applications
States of quantum systems and their liftings
Algebraic delocalization for the Schrödinger equation on large tori
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