5 papers
Absence of non-compactly supported minimisers for the Lieb-Oxford bound
Simone Di Marino, Rodrigue Lelotte
We prove the minimisers of the Lieb-Oxford bound (if any) for a fixed (and finite) number of particles are necessarily compactly supported, extending a result proved by…
A land of monotone plenty, bis repetita: from classical to weak optimal transport
Virginie Ehrlacher, Rodrigue Lelotte, Luca Nenna
The celebrated c-cyclical monotonicity property is shown to boil down to the zeroth-order optimality condition for the optimal transport problem. More precisely, we show that optim…
Phase transitions in one-dimensional Riesz gases with long-range interaction
Rodrigue Lelotte
We provide numerical evidence for the existence of phase transitions with respect to the temperature in the one-dimensional Riesz gases with non-singular pair interaction, that is…
Asymptotics of the Kantorovich Potential for the Optimal Transport with Coulomb Cost
Rodrigue Lelotte
We prove a conjecture regarding the asymptotic behavior at infinity of the Kantorovich potential for the Multimarginal Optimal Transport with Coulomb and Riesz costs.
An external dual charge approach to the optimal transport with Coulomb cost
Rodrigue Lelotte
In this paper, we study the multimarginal optimal transport with Coulomb cost, also known in the physics literature as the Strictly-Correlated Electrons (SCE) functional. We prove…