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math.SP2025
Geometric Criteria for Essential Self-Adjointness of Discrete Hodge Laplacians on Weighted Simplicial Complexes
Marwa Ennaceur, Amel Jadlaoui
We develop a geometric framework for the essential self-adjointness (ESA) of discrete Hodge Laplacians on weighted simplicial complexes of arbitrary dimension. Three notions of …
math.SP2025
Hodge Laplacians on Weighted Simplicial Complexes: Forms, Closures, and Bounded Realizations
Marwa Ennaceur, Amel Jadlaoui
We establish operator-norm bounds for discrete Hodge Laplacians on weighted flag complexes of a fixed dimension , whose -simplices are the -cliques of a weighted graph…
math.SP2019
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…