Author

Gilad Sofer

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Preprint Oct 2026

Zero measure Cantor spectrum for aperiodic metric tiling graphs

We study a family of aperiodic metric graphs generated by one-dimensional tilings. We prove that, generically, the spectrum of the associated Kirchhoff Laplacian has Lebesgue measure zero and, apart from a discrete set of isolated eigenvalues, is a generalized Cantor set. For a large subclass of these graphs, we furthe...

Ram Band, Gilad Sofer · 0 citations

Preprint Aug 2026

Spectral properties of aperiodic metric and discrete graphs

In this thesis, we study the spectral properties of dynamically defined aperiodic metric and discrete graphs. Our goal is to determine to what extent spectral properties of discrete one-dimensional ergodic Schr\"odinger operators persist when the aperiodicity is manifested through the geometry rather than through a pot...

Gilad Sofer · 1 citation