Asymptotics of analytic torsion for hyperbolic three--manifolds

We prove that for certain sequences of hyperbolic three--manifolds with cusps which converge to hyperbolic three--space in a weak ("Benjamini-Schramm") sense and certain coefficient systems the regularized analytic torsion approximates the $L^2$-torsion of the universal cover under an additional hypothesis. We also prove an asymptotic equality between the former and some Reidemeister torsion of the truncated manifolds.