12 citations · 49 across the 10 of their papers we have counts for
10 papers
Face volume densities of positive-intensity and ideal Poisson--Voronoi tessellations in hyperbolic spaces
Matteo D'Achille, Christoph Thäle
We determine analytically for all the -volume densities of a Poisson--Voronoi tessellation of intensity in the -dimensional hyperbolic space of…
Extremal Ising Gibbs States on Lobachevsky lattices
Matteo D'Achille, Loren Coquille, Arnaud Le Ny
We exhibit an uncountable family of extremal inhomogeneous Gibbs measures of the low temperature Ising model on regular tilings of the hyperbolic plane. These states arise as low t…
Decimations for One- and Two-dimensional Ising and Rotator Models II: Continuous versus Discrete Symmetries
Matteo D'Achille, Arnaud Le Ny, Aernout C. D. van Enter
We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still…
Decimations for Two-dimensional Ising and Rotator Models I
Matteo D'Achille, Aernout C. D. van Enter, Arnaud Le Ny
We extend proofs of non-Gibbsianness of decimated Gibbs measures at low temperatures to include long-range, as well as vector-spin interactions. Our main tools consist in a two-dim…
Almost Gibbsian Measures on a Cayley Tree
Matteo D'Achille, Arnaud Le Ny
We consider the ferromagnetic n.n Ising model on Cayley trees in absence of external fields submitted to a modified majority rule transformation with overlapping cells already know…
Random assignment problems on manifolds
Dario Benedetto, Emanuele Caglioti, Sergio Caracciolo +3
We consider the assignment problem between two sets of random points on a smooth, two-dimensional manifold of unit area. It is known that the average cost scales as $E_Ω(N)…
The Dyck bound in the concave 1-dimensional random assignment model
Sergio Caracciolo, Matteo P. D'Achille, Vittorio Erba +1
We consider models of assignment for random blue points and red points on an interval of length , in which the cost for connecting a blue point in to a red point in…
Anomalous scaling of the optimal cost in the one-dimensional random assignment problem
Sergio Caracciolo, Matteo D'Achille, Gabriele Sicuro
We consider the random Euclidean assignment problem on the line between two sets of random points, independently generated with the same probability density function .…
Random Euclidean matching problems in one dimension
Sergio Caracciolo, Matteo D'Achille, Gabriele Sicuro
We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the probl…
Finite-size corrections in the random assignment problem
Sergio Caracciolo, Matteo P. D'Achille, Enrico M. Malatesta +1
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…