Probabilistic positional association of astrophysical sources between catalogs

We describe a simple probabilistic method to cross-identify astrophysical sources from different catalogs and provide the probability that a source is associated with a source from another catalog or that it has no counterpart. When the positional uncertainty in one of the catalog is unknown, this method may be used to derive its typical value and even to study its dependence on the size of objects. It may also be applied when the true centers of a source and of its counterpart at another wavelength do not coincide. We extend this method to the case when there are only one-to-one associations between the catalogs.