Remarks on periodic Jacobi matrices on trees

Jacob S. Christiansen, Barry Simon, Maxim Zinchenko

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2 Citations (SciVal)


We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well-known gap in the spectrum of the Laplacian on the upper half-plane with a hyperbolic metric. We make some conjectures about antibound states and make an interesting observation for the so-called rg-model where the underlying graph has r red and g green vertices and where any two vertices of different colors are connected by a single edge.

Original languageEnglish
Article number042101
JournalJournal of Mathematical Physics
Issue number4
Publication statusPublished - 2021

Subject classification (UKÄ)

  • Mathematics


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