Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Nenna, Luca"'
We provide the first counter-example showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This property had been conjectured to hold for decades and it plays an
Externí odkaz:
http://arxiv.org/abs/2409.08632
Autor:
De Pascale, Luigi, Nenna, Luca
We propose a MFG model with quadratic Hamiltonian involving $N$ populations. This results in a system of $N$ Hamilton-Jacobi-Bellman and $N$ Fokker-Planck equations with non-local interactions. As in the classical case we introduce an Eulerian variat
Externí odkaz:
http://arxiv.org/abs/2408.03118
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two marginal problem
Externí odkaz:
http://arxiv.org/abs/2403.20238
Autor:
Nenna, Luca, Pegon, Paul
Publikováno v:
Canadian Journal of Mathematics, March 2024, First View, pp. 1-21
We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter $\varepsilon$ tends to $0$. We establish lower and upper bounds on the difference with the u
Externí odkaz:
http://arxiv.org/abs/2307.03023
Autor:
Ehrlacher, Virginie, Nenna, Luca
The aim of this paper is to present new sparsity results about the so-called Lieb functional, which is a key quantity in Density Functional Theory for electronic structure calculations of molecules. The Lieb functional was actually shown by Lieb to b
Externí odkaz:
http://arxiv.org/abs/2306.00806
Given a wave-function minimizing the Levy-Lieb functional, the intent of this short note is to give an estimate of the probability of the particles being in positions $(x_1, \ldots, x_N)$ in the $\delta$-close regime $D_{\delta}= \cup_{i \neq j} \{|x
Externí odkaz:
http://arxiv.org/abs/2303.00496
Autor:
Nenna, Luca, Pass, Brendan
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the number of ma
Externí odkaz:
http://arxiv.org/abs/2212.12492
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an equivalence
Externí odkaz:
http://arxiv.org/abs/2211.07694
Autor:
Nenna, Luca, Pass, Brendan
This note is devoted to study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by minimisation of some cost related to Optimal Transport. In particular we focus on the case of an Optimal Transport term be
Externí odkaz:
http://arxiv.org/abs/2209.14888
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible $N$'s, wh
Externí odkaz:
http://arxiv.org/abs/2201.06859