In this paper we investigate the L 1-Liouville property, underlining its connection with
stochastic completeness and other structural features of the graph. We give a …

Hardy inequality and asymptotic eigenvalue distribution for discrete Laplacians -
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We complete the understanding of the question of the essential self-adjoitness and non-
essential self-adjointness of the discrete Laplacian acting on 1-forms. We also discuss the …

The notions of magnetic difference operator defined on weighted graphs or magnetic
exterior derivative are discrete analogues of the notionof covariant derivative on sections of …

The notions of magnetic difference operator defined on weighted graphs or magnetic
exterior derivative are discrete analogues of the notion of covariant derivative on sections of …

En mécanique quantique relativiste, l'étude du comportement en temps long des solutions
de l'équation de Schrödinger est déterminante. Un principe d'absorption limite (Limiting …

We present the theory of positive commutator and its recent improvements. We discuss
applications to the spectral analysis of magnetic Laplacians on manifolds, singular Dirac …