Algebraic properties of the Fermi variety for periodic graph operators
We present a method to estimate the number of irreducible components of the Fermi
varieties of periodic Schrödinger operators on graphs in terms of suitable asymptotics. Our …
varieties of periodic Schrödinger operators on graphs in terms of suitable asymptotics. Our …
A useful formula for periodic Jacobi matrices on trees
J Banks, J Breuer, J Garza-Vargas… - Proceedings of the …, 2024 - National Acad Sciences
We introduce a function of the density of states for periodic Jacobi matrices on trees and
prove a useful formula for it in terms of entries of the resolvent of the matrix and its “half-tree” …
prove a useful formula for it in terms of entries of the resolvent of the matrix and its “half-tree” …
Flat bands of periodic graphs
We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate
eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support …
eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support …
Universality of free random variables: atoms for non-commutative rational functions
Abstract Consider a tuple (Y 1,…, Y d) of normal operators in a tracial operator algebra
setting with prescribed sizes of the eigenspaces for each Y i. We address the question what …
setting with prescribed sizes of the eigenspaces for each Y i. We address the question what …
Remarks on periodic Jacobi matrices on trees
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 …
gap of such operators analogous to the well-known gap in the spectrum of the Laplacian on …
Spectra of infinite graphs via freeness with amalgamation
J Garza-Vargas, A Kulkarni - arXiv preprint arXiv:1912.10137, 2019 - arxiv.org
We use tools from free probability to study the spectra of Hermitian operators on infinite
graphs. Special attention is devoted to universal covering trees of finite graphs. For …
graphs. Special attention is devoted to universal covering trees of finite graphs. For …
Spectra of infinite graphs via freeness with amalgamation
J Garza-Vargas, A Kulkarni - Canadian Journal of Mathematics, 2023 - cambridge.org
We use tools from free probability to study the spectra of Hermitian operators on infinite
graphs. Special attention is devoted to universal covering trees of finite graphs. For …
graphs. Special attention is devoted to universal covering trees of finite graphs. For …
Spectral Gaps for Jacobi Matrices on Graphs
J Breuer, E Seelig - arXiv preprint arXiv:2402.07202, 2024 - arxiv.org
arXiv:2402.07202v1 [math.SP] 11 Feb 2024 Page 1 arXiv:2402.07202v1 [math.SP] 11 Feb
2024 Spectral Gaps for Jacobi Matrices on Graphs Jonathan Breuer and Eyal Seelig ∗ In …
2024 Spectral Gaps for Jacobi Matrices on Graphs Jonathan Breuer and Eyal Seelig ∗ In …
Periodic boundary conditions for periodic Jacobi matrices on trees
We consider matrices on infinite trees which are universal covers of Jacobi matrices on finite
graphs. We are interested in the question of the existence of sequences of finite covers …
graphs. We are interested in the question of the existence of sequences of finite covers …