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              <p>In the first paper of this series we studied the asymptotic behavior of Betti numbers, twisted torsion and other spectral invariants for sequences of lattices in Lie groups G. A key element of our work was the study of invariant random subgroups (IRSs) of G. Any sequence of lattices has a subsequence converging to an IRS, and when G has higher rank, the Nevo-Stuck-Zimmer theorem classifies all IRSs of G. Using the classification, one can deduce asymptotic statments about spectral invariants of lattices. When G has real rank one, the space of IRSs is more complicated. We construct here several uncountable families of IRSs in the groups SO(n, 1), n ≥ 2. We give dimension-specific constructions when n = 2, 3, and also describe a general gluing construction that works for every n. Part of the latter contruction is inspired by Gromov and Piatetski-Shapiro's construction of nonarithmetic lattices in SO(n, 1).</p>
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              <p>Dans un travail précédent nous avons utilisé le théorème de Nevo--Stück--Zimmer pour obtenir une classification très simples des sous-groupes aléatoire invariants (IRS) des groupes de Lie de rang supérieur et en déduire des résultats de convergence pour les espaces localement symétriques. Le but de cet article est d'étudier l'espace des IRS pour les groupes SO(n, 1) qui sont de rang réel 1. Nous montrons que l'espace des IRS y est beucoup plus compliqué que dans le cas de rang supérieur. En dimension 2 et 3 nous donnons des constructions spécifiques et en toutes les dimensions une construction inspirée par les exemples de varaiétés non-arithmétiques de Gromov--Piatetski-Shapiro.</p>
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