Ergodic theory of affine isometric actions on Hilbert spaces

DOI10.1007/s00039-021-00584-2zbMath1505.37012arXiv1911.04272OpenAlexW2983249390WikidataQ114231703 ScholiaQ114231703MaRDI QIDQ2126275

Yuki Arano, Yusuke Isono, Amine Marrakchi

Publication date: 19 April 2022

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.04272

zbMATH Keywords

phase transitiontreesnonsingular actionGaussian measureorthogonal representationamenability in sense of Zimmer

Mathematics Subject Classification ID

Geometric group theory (20F65) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Groups acting on trees (20E08) General groups of measure-preserving transformations and dynamical systems (37A15) Nonsingular (and infinite-measure preserving) transformations (37A40)

Related Items (8)

Nonsingular Poisson suspensions ⋮ Haagerup property and Kazhdan pairs via ergodic infinite measure preserving actions ⋮ Isometric actions on L_p-spaces: dependence on the value of p ⋮ Krieger’s type for ergodic non-singular Poisson actions of non-(T) locally compact groups ⋮ Phase transitions for non-singular Bernoulli actions ⋮ BERNOULLI ACTIONS OF TYPE III WITH PRESCRIBED ASSOCIATED FLOW ⋮ Nonsingular Gaussian actions: beyond the mixing case ⋮ Nonsingular Bernoulli actions of arbitrary Krieger type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Simple locally compact groups acting on trees and their germs of automorphisms.
• Quantum Ito's formula and stochastic evolutions
• Amenable hyperbolic groups
• The density at infinity of a discrete group of hyperbolic motions
• Property T and asymptotically invariant sequences
• Random walk in a random environment and first-passage percolation on trees
• The limit set of a Fuchsian group
• Bernoulli actions of type \(\mathrm{III}_{1}\) and \(L^2\)-cohomology
• Harmonic analysis, cohomology, and the large-scale geometry of amenable groups
• Finite-dimensional representations constructed from random walks
• Ergodicity and type of nonsingular Bernoulli actions
• On spectral characterizations of amenability
• Isometric group actions on Hilbert spaces: growth of cocycles
• Sur la norme des opérateurs de convolution
• On cocycle superrigidity for Gaussian actions
• Irreducible affine isometric actions on Hilbert spaces
• Mildly Mixing Actions of Locally Compact Groups
• Symmetric Random Walks on Groups
• Uniform Tree Lattices
• Property (T) and the Furstenberg entropy of nonsingular actions
• Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
• Amenable Actions of Groups
• Groups of automorphisms of trees and their limit sets
• A functional analysis proof of Gromov's polynomial growth theorem
• Positive definite functions and cut-off for discrete groups
• 𝐿²-Betti numbers of locally compact groups and their cross section equivalence relations
• The Exponent of Convergence of Poincaré Series
• Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

This page was built for publication: Ergodic theory of affine isometric actions on Hilbert spaces