Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
16 - Uniform Existence of the IDS on Lattices and Groups
Published online by Cambridge University Press: 14 August 2020
Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
Summary
We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a parameter.All results are illustrated with the example of eigenvalue counting functions converging to the integrated density of states.In this case, the convergence is uniform in the energy.
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- Analysis and Geometry on Graphs and Manifolds , pp. 445 - 478Publisher: Cambridge University PressPrint publication year: 2020