Almost all non-archimedean Kakeya sets have measure zero
  We study Kakeya sets over local non-archimedean fields with a probabilistic point of view: we define a probability measure on the set of Kakeya sets as above and prove that, according to this measure, almost all non-archimedean Kakeya sets are neglectable according to the Haar measure. We also discuss possible relations with the non-archimedean Kakeya conjecture. 
Xavier Caruso (IRMAR)
math.CO math.NT math.PR