Moment convergence of balanced P\'olya processes
  It is known that in an irreducible small P\'olya urn process, the composition of the urn after suitable normalization converges in distribution to a normal distribution. We show that if the urn also is balanced, this normal convergence holds with convergence of all moments, thus giving asymptotics of (central) moments. 
Svante Janson, Nicolas Pouyanne
math.PR