https://hal-ens-lyon.archives-ouvertes.fr/ensl-00189834Michel, JulienJulienMichelUMPA-ENSL - Unité de Mathématiques Pures et Appliquées - ENS Lyon - École normale supérieure - Lyon - CNRS - Centre National de la Recherche ScientifiqueConcentration for Young measures and conditioned Boolean modelHAL CCSD2007Point processesYoung measuressimulationmaximum entropy principleBoolean model[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Michel, Julien2007-11-22 14:49:152023-03-24 14:52:492007-11-22 15:46:50enPreprints, Working Papers, ...application/pdf1We 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.