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- GABRIELE SICURO
- 2014

In 1781 a French geometer, Gaspard Monge (1746–1818), published his Mémoire sur la théorie des déblais at des remblais, in which he discussed the following very simple problem. Let us suppose that we have a certain number of mines and the same number of deposits. We want to associate each mine to one deposit only (where the production of the considered mine… (More)

- Gabriele Sicuro, Piergiulio Tempesta
- Physical review. E
- 2016

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin… (More)

- Sergio Caracciolo, Gabriele Sicuro
- Physical review. E, Statistical, nonlinear, and…
- 2014

We discuss the equivalence relation between the Euclidean bipartite matching problem on the line and on the circumference and the Brownian bridge process on the same domains. The equivalence allows us to compute the correlation function and the optimal cost of the original combinatorial problem in the thermodynamic limit; moreover, we solve also the minimax… (More)

- Sergio Caracciolo, Carlo Lucibello, Giorgio Parisi, Gabriele Sicuro
- Physical review. E, Statistical, nonlinear, and…
- 2014

We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic prediction of the large N limit of the average cost in dimension d = 1,2 and of the subleading correction in higher… (More)

- Gabriele Sicuro, Peter Rapčan, Constantino Tsallis
- Physical review. E
- 2016

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the… (More)

- Carlo Lucibello, Giorgio Parisi, Gabriele Sicuro
- Physical review. E
- 2017

The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e., the optimal matching problem between points randomly distributed on a d-dimensional Euclidean space, where the cost to minimize depends on the… (More)

- Sergio Caracciolo, Matteo P D'Achille, Enrico M Malatesta, Gabriele Sicuro
- Physical review. E
- 2017

We analytically derive, in the context of the replica formalism, the first finite-size corrections to the average optimal cost in the random assignment problem for a quite generic distribution law for the costs. We show that, when moving from a power-law distribution to a Γ distribution, the leading correction changes both in sign and in its scaling… (More)

- Sergio Caracciolo, Gabriele Sicuro
- Physical review letters
- 2015

We propose a new approach for the study of the quadratic stochastic Euclidean bipartite matching problem between two sets of N points each, N≫1. The points are supposed independently randomly generated on a domain Ω⊂R^{d} with a given distribution ρ(x) on Ω. In particular, we derive a general expression for the correlation function and for the average… (More)

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