Limit theorems for sequences of random trees

Abstract

We consider a random tree and introduce a metric in the space of trees to define the ``mean tree'' as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

REvised version, 15 pages. An error on the parameter-range is corrected. Now z<m^{-3/2}