37 citations · 124 across the 19 of their papers we have counts for
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Spectral analysis of the Laplacian acting on discrete cusps and funnels
Nassim Athmouni, Marwa Ennaceur, Sylvain Golenia
We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a pr…
Magnetic sparseness and Schrödinger operators on graphs
Michel Bonnefont, Sylvain Golénia, Matthias Keller +2
We study magnetic Schrödinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnet…
Propagation estimates in the one-commutator theory
Sylvain Golenia, Marc-Adrien Mandich
In the abstract framework of Mourre theory, the propagation of states is understood in terms of a conjugate operator . A powerful estimate has long been known for Hamiltonians h…
The adjacency matrix and the discrete Laplacian acting on forms
Hatem Baloudi, Sylvain Golenia, Aref Jeribi
We study the relationship between the adjacency matrix and the discrete Laplacian acting on 1-forms. We also prove that if the adjacency matrix is bounded from below it is not nece…
Essential spectrum and Weyl asymptotics for discrete Laplacians
Michel Bonnefont, Sylvain Golenia
In this paper, we investigate spectral properties of discrete Laplacians. Our study is based on the Hardy inequality and the use of super-harmonic functions. We recover and improve…
Eigenvalue asymptotics for Schrödinger operators on sparse graphs
Michel Bonnefont, Sylvain Golenia, Matthias Keller
We consider Schrödinger operators on sparse graphs. The geometric definition of sparseness turn out to be equivalent to a functional inequality for the Laplacian. In consequence, s…