Pál Révész - Critical branching Wiener process in the d-dimensional Eucledean space (3 talks)

Consider a particle which executes a critical branching Wiener process. Assume that this particle is living till time T. Then we investigate the empirical distribution function defined by the locations of the particles at time T as well as some functionals of this distribution. A related question is the behaviour of the probability that at least one particle is located in a given ball. We also consider the properties of a critical branching random field. That is we have a Poisson point process in time 0 and the points of this field execute independent branching Wiener processes. A typical question is to investigate the radius of the smallest ball around the origin which consists of at least one particle at time T.