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math.PR2021
Almost sure recovery in quasi-periodic structures
Mircea Petrache, Rodolfo Viera
We study random perturbations of quasi-periodic uniformly discrete sets in the -dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a qua…
math.MG2021
Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings
Giacomo Del Nin, Mircea Petrache
We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimet…