Local existence of solutions to randomized Gross-Pitaevskii hierarchies

independently randomized Gross-Pitaevskii hierarchy and the , which were first introduced in the author's joint work with Staffilani (2013). For these hierarchies, we construct local-in-time low-regularity solutions in spaces which contain a random component. The constructed density matrices will solve the full randomized hierarchies, thus extending the results from the author and Staffilani's joint work, where solutions solving arbitrarily long subhierarchies were given.