Phase transitions for nonsingular Bernoulli actions

2022/10/11 by Tey Berendschot, Berendschot, Tey
Mathematics · Physics and Astronomy · #37A40 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2210.05500

openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the phase transition results for nonsingular Gaussian actions introduced in arXiv:1911.04272, we prove several phase transition results for nonsingular Bernoulli actions. For generalized Bernoulli actions arising from groups acting on trees, we are able to give a very precise description of their ergodic theoretical properties in terms of the Poincaré exponent of the group.

Citations

• Ergodic theory of affine isometric actions on Hilbert spaces

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