94 citations · 448 across the 40 of their papers we have counts for
49 papers
Concentration for random Euclidean combinatorial optimization
Matteo D'Achille, Francesco Mattesini, Dario Trevisan
We prove concentration bounds for random Euclidean combinatorial optimization problems with --costs. For bipartite matching and for the (mono- and bi-partite) traveling salesper…
Boundedness of Riesz transforms on $\RCD(K, \infty)$ spaces
Andrea Carbonaro, Luca Tamanini, Dario Trevisan
For , we prove the -boundedness of the Riesz transform operators on metric measure spaces with Riemannian Ricci curvature bounded from below, without any restricti…
Quantum Optimal Transport: Quantum Channels and Qubits
Giacomo De Palma, Dario Trevisan
These notes are based on the lectures given by the second author at the School on Optimal Transport on Quantum Structures at Erdös Center in September 2022. The focus of the exposi…
Wasserstein Asymptotics for Brownian Motion on the Flat Torus and Brownian Interlacements
Mauro Mariani, Dario Trevisan
We study the large time behavior of the optimal transportation cost towards the uniform distribution, for the occupation measure of a stationary Brownian motion on the flat torus i…
On the concave one-dimensional random assignment problem and Young integration theory
Michael Goldman, Dario Trevisan
We investigate the one-dimensional random assignment problem in the concave case, i.e., the assignment cost is a concave power function, with exponent , of the distance betw…
The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
Giacomo De Palma, Dario Trevisan
We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice , which we call specific quantum distance. The proposa…
Optimal transport methods for combinatorial optimization over two random point sets
Michael Goldman, Dario Trevisan
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in where the edge cost between two poin…
Wasserstein Asymptotics for the Empirical Measure of Fractional Brownian Motion on a Flat Torus
Martin Huesmann, Francesco Mattesini, Dario Trevisan
We establish asymptotic upper and lower bounds for the Wasserstein distance of any order between the empirical measure of a fractional Brownian motion on a flat torus and…
Viscosity solutions of Hamilton-Jacobi equation in spaces and applications to large deviations
Nicola Gigli, Luca Tamanini, Dario Trevisan
The aim of this paper is twofold. - In the setting of RCD(K,) metric measure spaces, we derive uniform gradient and Laplacian contraction estimates along solutions of the v…
Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks
Andrea Basteri, Dario Trevisan
Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution a…
Infinite multidimensional scaling for metric measure spaces
Alexey Kroshnin, Eugene Stepanov, Dario Trevisan
For a given metric measure space we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimen…
On exterior differential systems involving differentials of Hölder functions
Eugene Stepanov, Dario Trevisan
We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional…
On the quadratic random matching problem in two-dimensional domains
Luigi Ambrosio, Michael Goldman, Dario Trevisan
We investigate the average minimum cost of a bipartite matching, with respect to the squared Euclidean distance, between two samples of n i.i.d. random points on a bounded Lipschit…
On Minimum Spanning Trees for Random Euclidean Bipartite Graphs
Mario Correddu, Dario Trevisan
We consider the minimum spanning tree problem on a weighted complete bipartite graph whose vertices are random, i.i.d. uniformly distributed points in th…
The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems
Giacomo De Palma, Dario Trevisan
We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear c…
Reconstruction of manifold embeddings into Euclidean spaces via intrinsic distances
Nikita Puchkin, Vladimir Spokoiny, Eugene Stepanov +1
We consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic…
Lie brackets of nonsmooth vector fields and commutation of their flows
Chiara Rigoni, Eugene Stepanov, Dario Trevisan
It is well-known that the flows generated by two smooth vector fields commute, if the Lie bracket of these vector fields vanishes. This assertion is known to extend to Lipschitz co…
The Quantum Wasserstein Distance of Order 1
Giacomo De Palma, Milad Marvian, Dario Trevisan +1
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of qudits. The proposal recovers the Hamming distance for the vectors of the canonical…
Convergence of asymptotic costs for random Euclidean matching problems
Michael Goldman, Dario Trevisan
We investigate the average minimum cost of a bipartite matching between two samples of n independent random points uniformly distributed on a unit cube in d 3 dimensions, whe…
Towards geometric integration of rough differential forms
Eugene Stepanov, Dario Trevisan
We provide a draft of a theory of geometric integration of rough differential forms which are generalizations of classical (smooth) differential forms to similar objects with very…
Integration of nonsmooth -forms: from Young to Itô and Stratonovich
Giovanni Alberti, Eugene Stepanov, Dario Trevisan
We show that geometric integrals of the type can be defined over a two-dimensional domain when the functions , , $g^2\colon \mathbb{R}^…
Quantum optimal transport with quantum channels
Giacomo De Palma, Dario Trevisan
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a tran…
On the optimal map in the 2-dimensional random matching problem
Luigi Ambrosio, Federico Glaudo, Dario Trevisan
We show that, on a -dimensional compact manifold, the optimal transport map in the semi-discrete random matching problem is well-approximated in the -norm by identity plus…
Gaussian optimizers for entropic inequalities in quantum information
Giacomo De Palma, Dario Trevisan, Vittorio Giovannetti +1
We survey the state of the art for the proof of the quantum Gaussian optimizer conjectures of quantum information theory. These fundamental conjectures state that quantum Gaussian…