Limit theorems for sequences of random trees

2004/06/14 by David Balding, Pablo A. Ferrari, Balding, David +5 · 1 citation
Mathematics · #60D05 60F17 60D05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60D05 #msc:60F17

paper · pdf · doi:10.48550/arxiv.math/0406280

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

arxiv created 2007/05/01 · arxiv updated 2009/12/01

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.

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