A NOTE ON THE NORMS OF TRANSITION OPERATORS ON LAMPLIGHTER GRAPHS AND GROUPS

DOI10.1142/S0218196705002591zbMath1084.05034OpenAlexW2023188158MaRDI QIDQ3379496

Wolfgang Woess

Publication date: 6 April 2006

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196705002591

zbMATH Keywords

spectral radiusrandom walkwreath product

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Extensions, wreath products, and other compositions of groups (20E22)

Related Items

Wreath product of matrices ⋮ Radon transforms and lamplighter random walks ⋮ Harmonic analysis of finite lamplighter random walks ⋮ Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks ⋮ On the spectrum of lamplighter groups and percolation clusters ⋮ Total distance, Wiener index and opportunity index in wreath products of star graphs ⋮ The phase transition for dyadic tilings ⋮ Some degree and distance-based invariants of wreath products of graphs ⋮ Wreath product of a complete graph with a cyclic graph: topological indices and spectrum

Cites Work

• Spectral computations on lamplighter groups and Diestel-Leader graphs
• Amenability, unimodularity, and the spectral radius of random walks on infinite graphs
• Automorphism groups of graphs as topological groups
• Polynomidentitäten und Permutationsdarstellungen lokalkompakter Gruppen
• Transition operators, groups, norms, and spectral radii
• The spectral measure of certain elements of the complex group ring of a wreath product
• Isoperimetric Inequalities and Decay of Iterated Kernels for Almost-transitive Markov Chains
• The lamplighter group as a group generated by a 2-state automaton, and its spectrum