Local hitting and conditioning in symmetric interval partitions

By a symmetric interval partition we mean a perfect, closed random set [Xi] in [0,1] of Lebesgue measure 0, such that the lengths of the connected components of [Xi]c occur in random order. Such sets are analogous to the regenerative sets on , and in particular there is a natural way to define a corresponding local time random measure [xi] with support [Xi]. In this paper, the author's recently developed duality theory is used to construct versions of the Palm distributions Qx of [xi] 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.