Infinite-body optimal transport with Coulomb cost.

We introduce and analyze symmetric infinite-body optimal transport (OT) problems with cost function of pair potential form. We show that for a natural class of such costs, the optimizer is given by the independent product measure all of whose factors are given by the one-body marginal. This is in striking contrast to standard finite-body OT problems, in which the optimizers are typically highly correlated, as well as to infinite-body OT problems with Gangbo-Swiech cost.

N-density representability and the optimal transport limit of the Hohenberg-Kohn functional.

We derive and analyze a hierarchy of approximations to the strongly correlated limit of the Hohenberg-Kohn functional. These "density representability approximations" are obtained by first noting that in the strongly correlated limit, N-representability of the pair density reduces to the requirement that the pair density must come from a symmetric N-point density. One then relaxes this requirement to the existence of a representing symmetric k-point density with k < N.

Should females prefer to mate with low-quality males?

We analyse a model of mate choice when males differ in reproductive quality and provide care for their offspring. Females choose males on the basis of the success they will obtain from breeding with them and a male chooses his care time on the basis of his quality so as to maximise his long-term rate of reproductive success. We use this model to establish whether high-quality males should devote a longer period of care to their broods than low-quality males and whether females obtain greater reproductive success from mating with higher quality males.