Random finite covers of manifolds with Ricci curvature bounded below have no new Laplacian eigenvalues in [0,Λ] when the fundamental group satisfies strong convergence of permutation representations.
Baumslag, Residually free groups, Proc
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On the spectral stability of finite coverings
Random finite covers of manifolds with Ricci curvature bounded below have no new Laplacian eigenvalues in [0,Λ] when the fundamental group satisfies strong convergence of permutation representations.