The mean density of a random closed set Θ in R with Hausdorff dimension n is the Radon-Nikodym derivative of the expected measure E[H(Θ ∩ · )] induced by Θ with respect to the usual d-dimensional Lebesgue measure. We consider here inhomogeneous Boolean models with lower dimensional typical grain. Under general regularity assumptions on the typical grain, related to the existence of its Minkowsk...

We revisit the concept of spectral averaging and point out its origin in connection with one-parameter subgroups of SL2(R) and the corresponding Möbius transformations. In particular, we identify exponential Herglotz representations as the basic ingredient for the absolute continuity of average spectral measures with respect to Lebesgue measure and the associated spectral shift function as the ...