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SUMMARY:Maximal clades in random binary search trees - Svante Janson (Upps
 ala University)
DTSTART:20150226T143000Z
DTEND:20150226T153000Z
UID:TALK58231@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Define a clade in a binary tree as the set of external nodes t
 hat are descendants of the parent of some external node. (This has a biolo
 gical background\, but I am no expert on that.) If we consider only the in
 ternal\nnodes\, a clade thus corresponds to a node with less than two chil
 dren. Furthermore\, a maximal clade corresponds to a node with less than t
 wo children\, but with all ancestors having two children.\n\nWe study the 
 number of maximal clades in a  random binary search tree (or\, equivalentl
 y\, in a random phylogenetic tree with the Yule--Harding model). We use pr
 obabilistic methods to reprove and extend earlier results on moment\nasymp
 totics and asymptotic normality. In particular\, we give an explanation of
  the curious phenomenon  observed by Drmota\, Fuchs and Lee (2014) that as
 ymptotic normality holds\, but one should normalize using half the varianc
 e.\n
LOCATION:MR12
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