Related papers: Isospectral Reduction in Infinite Graphs
We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for $C_0$-semigroups of…
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…
The goal of the paper is to apply the general operator theoretic construction known as the Schur complement for computation of the spectrum of certain infinite graphs which can be viewed as finite graphs with the ray attached to them. The…
Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual…
We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…
We present the main concepts and results for Graph Directed Markov Systems that have a finitely irreducible incidence matrix. We then see how these results change when the incidence matrix is not assumed to be finitely irreducible.
In 1999, Benjamini, Lyons, Peres, and Schramm introduced a notion of weighted-amenability for transitive graphs that is equivalent to the amenability of its automorphism group. For unimodular graphs this notion coincides with classical…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such…
The Bandwidth Theorem of B\"ottcher, Schacht and Taraz [Mathematische Annalen 343 (1), 175-205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this…
We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and derive a new formula for the Stieljes transform of the spectral…
Chudnovsky, Kim, Oum, and Seymour recently established that any prime graph contains one of a short list of induced prime subgraphs [1]. In the present paper we reprove their theorem using many of the same ideas, but with the key…
How might one "reduce" a graph? That is, generate a smaller graph that preserves the global structure at the expense of discarding local details? There has been extensive work on both graph sparsification (removing edges) and graph…
Given a collection $\mathcal{G}=(G_1,\dots, G_h)$ of graphs on the same vertex set $V$ of size $n$, an $h$-edge graph $H$ on the vertex set $V$ is a $\mathcal{G}$-transversal if there exists a bijection $\lambda : E(H) \rightarrow [h]$ such…
We count invertible Schr\"odinger operators (perturbations by diagonal matrices of the adjacency matrix) over finite fieldsfor trees, cycles and complete graphs.This is achieved for trees through the definition and use of local invariants…
We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this…
The well-known Kamowitz - Scheinberg theorem states that if $U$ is an automorphism of a commutative semi-simple Banach algebra and $U^n \neq I, n \in \mathds{N}$, then the spectrum of $U$ contains the unit circle. In this paper we present…
We study in how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator…
We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not…
We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…
We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…