7 papers
Stability and robustness of mathematical quasicrystals under statistical convergence
Rodolfo Viera
In this work we address the stability and robustness of uniformly discrete point sets in Euclidean spaces. Firstly, we prove that if a sequence of point configurations contained in…
A remark on dimensionality reduction in discrete subgroups
Rodolfo Viera
In this short note, we prove a version of the Johnson-Lindenstrauss flattening Lemma for point sets taking values in discrete subgroups. More precisely, given $d,λ_0,N_0\in\mathbb{…
On rectifiability of Delone sets in intermediate regularity
Irene Inoquio-Renteria, Rodolfo Viera
In this work, we deal with Delone sets and their rectifiability under different classes of regularity. By pursuing techniques developed by Rivière and Ye, and Aliste-Prieto, Corone…
Effective recovery of Fourier spectra and spectral approximation by finite groups
Mircea Petrache, Rodolfo Viera
We prove a result on approximate recovery, with high probability, of subgroups of a finite nonabelian group from their random perturbations. We use this for ad-hoc sequences of…
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…
Delone sets that are not rectifiable under Lipschitz co-uniformly continuous bijections
Rodolfo Viera
We prove that there exist Delone sets in , , which cannot be mapped onto the standard lattice by Lipschitz co-uniformly continuous bijections…
Densities non-realizable as the Jacobian of a 2-dimensional bi-Lipschitz map are generic
Rodolfo Viera
It is shown that, generically, a positive continuous functions cannot be written as the derivative of a bi-Lipschitz plane homeomorphism. The same is proved for generic bounded fun…