Limit distribution of the degrees in scaled attachment random recursive trees

Document Type: Research Paper

Author

Department of Statistics, Zanjan University, Zanjan, Iran

Abstract

We study the limiting distribution of the degree of a
given node in a scaled attachment random recursive tree, a
generalized random recursive tree, which is introduced by Devroye
et. al (2011). In a scaled attachment random recursive tree, every
node $i$ is attached to the node labeled $lfloor iX_i
floor$
where $X_0$, $ldots$ , $X_n$ is a sequence of i.i.d. random
variables, with support in [0, 1) and distribution function $F$.
By imposing a condition on $F$, we show that the degree of a given
node is asymptotically normal.

Keywords

Main Subjects



Volume 39, Issue 5
September and October 2013
Pages 1031-1036
  • Receive Date: 19 May 2012
  • Revise Date: 20 September 2012
  • Accept Date: 20 September 2012