Local hitting and conditioning in symmetric interval partitions

By a symmetric interval partition we mean a perfect, closed random set Ξ in [0,1] of Lebesgue measure 0, such that the lengths of the connected components of Ξc occur in random order. Such sets are analogous to the regenerative sets on R+, and in particular there is a natural way to define a corresponding local time random measure ξ with support Ξ. In this paper, the authorʹs recently developed duality theory is used to construct versions of the Palm distributions Qx of ξ with attractive continuity and approximation properties. The results are based on an asymptotic formula for hitting probabilities and a delicate construction and analysis of conditional densities.