Spectral distribution and \(L^{2}\)-isoperimetric profile of Laplace operators on groups

DOI10.1007/s00208-011-0724-6zbMath1268.43001arXiv0901.0271OpenAlexW2092735377MaRDI QIDQ453315

Roman Sauer, Christophe Pittet, Alexander D. Bendikov

Publication date: 19 September 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.0271

zbMATH Keywords

finite second momentfinitely generated groupFolner's function on groupSpectral distribution of Laplace operator

Mathematics Subject Classification ID

Measures on groups and semigroups, etc. (43A05) Diffusion processes and stochastic analysis on manifolds (58J65) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (17)

On spectral properties of the Schreier graphs of the Thompson group 𝐹 ⋮ Spectral properties of a class of random walks on locally finite groups ⋮ On the lattice of subgroups of the lamplighter group ⋮ Separation profile, isoperimetry, growth and compression ⋮ Self-similar groups and holomorphic dynamics: renormalization, integrability, and spectrum ⋮ Asymptotic behaviors of random walks on countable groups ⋮ On a class of Markov semigroups on discrete ultra-metric spaces ⋮ Spectral distribution and \(L^{2}\)-isoperimetric profile of Laplace operators on groups ⋮ Random walk on a discrete Heisenberg group ⋮ Speed of random walks, isoperimetry and compression of finitely generated groups ⋮ A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces ⋮ The Liouville property and Hilbertian compression ⋮ Random walks driven by low moment measures ⋮ Sub-dominant Cogrowth Behavior and the Viability of Deciding Amenability Numerically ⋮ Random walks among time increasing conductances: heat kernel estimates ⋮ Some Spectral and Geometric Aspects of Countable Groups ⋮ Random walks on free solvable groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral distribution and \(L^{2}\)-isoperimetric profile of Laplace operators on groups
• Invariance of return probabilities on locally compact groups
• Spectral computations on lamplighter groups and Diestel-Leader graphs
• Piecewise automatic groups.
• Entropy and isoperimetry for linear and non-linear group actions.
• Ultracontractivity and embedding into \(L^\infty\)
• Random walks on discrete groups: Boundary and entropy
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Von Neumann spectra near zero
• Isoperimetricity for groups and manifolds
• On-diagonal lower bounds for heat kernels and Markov chains
• Random walks on finite rank solvable groups.
• The isoperimetric profile of homogeneous Riemannian manifolds.
• The spectral measure of certain elements of the complex group ring of a wreath product
• On random walks on wreath products
• Isometric Riemannian manifolds at infinity
• Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks
• Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs
• On a question of Atiyah
• On groups with full Banach mean value
• Full Banach Mean Values on Countable groups.
• A Survey on Spectra of infinite Graphs
• Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks
• On the stability of the behavior of random walks on groups
• A geometric approach to on-diagonal heat kernel lower bounds on groups.

This page was built for publication: Spectral distribution and \(L^{2}\)-isoperimetric profile of Laplace operators on groups