36 citations · 112 across the 19 of their papers we have counts for
26 papers
The five gradients inequality on differentiable manifolds
S. Di Marino, S. Murro, E. Radici
The goal of this paper is to derive the so-called five gradients inequality for optimal transport theory for general cost functions on two class of differentiable manifolds: locall…
Universal diagonal estimates for minimizers of the Levy-Lieb functional
Simone Di Marino, Augusto Gerolin, Luca Nenna
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…
Optimal transport with nonlinear mobilities: a deterministic particle approximation result
Simone Di Marino, Lorenzo Portinale, Emanuela Radici
We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a sett…
Grand-Canonical Optimal Transport
Simone Di Marino, Mathieu Lewin, Luca Nenna
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals and is inspired of statistical mechanics. It consists in optim…
Representation theorems for normed modules
Simone Di Marino, Danka Lučić, Enrico Pasqualetto
In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework…
First order expansion in the semiclassical limit of the Levy-Lieb functional
Maria Colombo, Simone Di Marino, Federico Stra
We prove the conjectured first order expansion of the Levy-Lieb functional in the semiclassical limit, arising from Density Functional Theory (DFT). This is accomplished by interpr…
Global Lipschitz extension preserving local constants
Simone Di Marino, Nicola Gigli, Aldo Pratelli
The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while locally preserving the asymptotic Lipschitz constant. We then apply this results…
Optimal Transport losses and Sinkhorn algorithm with general convex regularization
Simone Di Marino, Augusto Gerolin
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and p…
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
Simone Di Marino, Danka Lučić, Enrico Pasqualetto
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, i…
JKO estimates in linear and non-linear Fokker-Planck equations, and Keller-Segel: L p and Sobolev bounds
Simone Di Marino, Filippo Santambrogio
We analyze some parabolic PDEs with different drift terms which are gradient flows in the Wasserstein space and consider the corresponding discrete-in-time JKO scheme. We prove wit…
An Optimal Transport approach for the Schrödinger bridge problem and convergence of Sinkhorn algorithm
Simone Di Marino, Augusto Gerolin
This paper exploit the equivalence between the Schrödinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the s…
Metric completion of with the right-invariant metric
Simone Di Marino, Andrea Natale, Rabah Tahraoui +1
We consider the group of smooth increasing diffeomorphisms Diff on the unit interval endowed with the right-invariant metric. We compute the metric completion of this space w…
Infinitesimal Hilbertianity of locally CAT()-spaces
Simone Di Marino, Nicola Gigli, Enrico Pasqualetto +1
We show that, given a metric space of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure on giving finite mass to bounded sets, t…
An entropy minimization approach to second-order variational mean-field games
Jean-David Benamou, Guillaume Carlier, Simone Di Marino +1
We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimi…
New characterizations of Sobolev metric spaces
Simone Di Marino, Marco Squassina
We provide new characterizations of Sobolev ad BV spaces in doubling and Poincare metric spaces in the spirit of the Bourgain-Brezis-Mironescu and Nguyen limit formulas holding in…
Linear Lipschitz and extension operators through random projection
Elia Bruè, Simone Di Marino, Federico Stra
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and functions. This way we prove more directl…
A tumor growth model of Hele-Shaw type as a gradient flow
Lénaïc Chizat, Simone Di Marino
In this paper, we characterize a degenerate PDE as the gradient flow in the space of nonnegative measures endowed with an optimal transport-growth metric. The PDE of concern, of He…
The entropic regularization of the Monge problem on the real line
Simone Di Marino, Jean Louet
We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance c(x, y) = |y -- x|. The selected plan at the limit is, a…
The strictly-correlated electron functional for spherically symmetric systems revisited
Michael Seidl, Simone Di Marino, Augusto Gerolin +3
The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this lim…
Perimeter as relaxed Minkowski content in metric measure spaces
Luigi Ambrosio, Nicola Gigli, Simone Di Marino
In this note we prove that on general metric measure spaces the perimeter is equal to the relaxation of the Minkowski content w.r.t.\ convergence in measure
Uniqueness issues for evolution equations with density constraints
Simone Di Marino, Alpár Richárd Mészáros
In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialis…
Optimal Transportation Theory with Repulsive Costs
Simone Di Marino, Augusto Gerolin, Luca Nenna
This paper intents to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions. We introduc…
Sobolev and BV spaces on metric measure spaces via derivations and integration by parts
Simone Di Marino
We develop a theory of BV and Sobolev Spaces via integration by parts formula in abstract metric spaces; the role of vector fields is played by Weaver's metric derivations. The def…
The p-Weak Gradient Depends on p
Simone Di Marino, Gareth Speight
Given a>0, we construct a weighted Lebesgue measure on R^n for which the family of non constant curves has p-modulus zero for p\leq 1+a but the weight is a Muckenhoupt A_p weight f…