\(L^{2}\)-spectral invariants and convergent sequences of finite graphs

DOI10.1016/j.jfa.2008.01.010zbMath1203.05068arXiv0709.1261OpenAlexW2012887473MaRDI QIDQ924662

Gábor Elek

Publication date: 19 May 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.1261

zbMATH Keywords

spectrumvon Neumann algebrasgraph sequences

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Applications of selfadjoint operator algebras to physics (46L60) Applications of functional analysis in statistical physics (46N55)

Related Items (13)

From quasirandom graphs to graph limits and graphlets ⋮ Metric measure geometry: An approach to high-dimensional and infinite-dimensional spaces ⋮ Delone dynamical systems and spectral convergence ⋮ The Ihara zeta function for infinite graphs ⋮ A Banach space-valued ergodic theorem for amenable groups and applications ⋮ Finite graphs and amenability ⋮ Convergence theorems for graph sequences ⋮ Sublinear Graph Approximation Algorithms ⋮ Parameter testing in bounded degree graphs of subexponential growth ⋮ A \(C^*\)-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and \(L^2\)-Betti numbers ⋮ Lamplighter groups and von Neumann‘s continuous regular ring ⋮ Uniform local amenability implies Property A ⋮ Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence

Cites Work

• The strong approximation conjecture holds for amenable groups
• Entropy and isomorphism theorems for actions of amenable groups
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Recurrence of distributional limits of finite planar graphs
• The combinatoral cost
• An ergodic theorem for Delone dynamical systems and existence of the integrated density of states
• Some remarks on discrete aperiodic Schrödinger operators
• Graph limits and parameter testing
• Approximating L²‐invariants and the Atiyah conjecture
• Growth of Self‐Similar Graphs
• NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
• The lamplighter group as a group generated by a 2-state automaton, and its spectrum

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