Cluster expansion of the resolvent for the Schrödinger operator on non-percolating graphs with applications to Simon-Spencer type theorems and localization
Summary: The paper contains a generalization of the well-known 1D results on the absence of the a.c. spectrum (in the spirit of the Simon-Spencer theorem) and localization to the wide class of ``non-percolating'' graphs, which include the Sierpiński lattice and quasi 1D trees. The main tools are cluster expansion of the resolvent and real analytic techniques (Kolmogorov's lemma and similar estimates).
scientific article; zbMATH DE number 6801916