Concentration for Young measures and conditioned Boolean model

We present a method for determining the probability that a given point lies in the vacant region of a Boolean model subject to the condition that this probability takes imposed values on certain points. This method is based on a characterisation of the intensity of the Boolean model as a Young measure, such that after discretisation a large deviations principle holds; this induces a concentration property which can be transposed for the Boolean model, yielding the maximum of entropy state satisfying the conditioning. The numerical computation of this Gibbs state gives the parameters of the conditioned Boolean model, and thus one can answer both numerically and theoretically to the problem of finding the vacancy function at any point. MSC 2000: primary 60G55, secondary 60D05, 60K40.