2 results
Continuum of allosteric actions for non-amenable surface groups
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 6 / June 2024
- Published online by Cambridge University Press:
- 19 July 2023, pp. 1581-1596
- Print publication:
- June 2024
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Let
$\Sigma $ be a closed surface other than the sphere, the torus, the projective plane or the Klein bottle. We construct a continuum of probability measure preserving ergodic minimal profinite actions for the fundamental group of 
$\Sigma $ that are topologically free but not essentially free, a property that we call allostery. Moreover, the invariant random subgroups we obtain are pairwise distincts.
Co-spectral radius of intersections
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 2 / February 2024
- Published online by Cambridge University Press:
- 17 April 2023, pp. 509-523
- Print publication:
- February 2024
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We study the behavior of the co-spectral radius of a subgroup H of a discrete group
$\Gamma $ under taking intersections. Our main result is that the co-spectral radius of an invariant random subgroup does not drop upon intersecting with a deterministic co-amenable subgroup. As an application, we find that the intersection of independent co-amenable invariant random subgroups is co-amenable.
