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  • Spectral estimates for infinite quantum graphs
    Kostenko, Aleksej Sergejevič, 1980- ; Nicolussi, Noema
    We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definition of the ... isoperimetric constant for quantum graphs and then prove the Cheeger-type estimate. Our definition of the isoperimetric constant is purely combinatorial and thus it establishes connections with the combinatorial isoperimetric constant, one of the central objects in spectral graph theory and in the theory of simple random walks on graphs. The latter enables us to prove a number of criteria for quantum graphs to be uniformly positive or to have purely discrete spectrum. We demonstrate our findings by considering trees, antitrees and Cayley graphs of finitely generated groups.
    Vir: Calculus of variations and partial differential equations. - ISSN 0944-2669 (Vol. 58, iss. 1, Feb. 2019, art. 15 (40 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 18836057

    Povezava(-e):

    https://doi.org/10.1007/s00526-018-1454-3
    DOI

vir: Calculus of variations and partial differential equations. - ISSN 0944-2669 (Vol. 58, iss. 1, Feb. 2019, art. 15 (40 str.))

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