scholarly journals Self-similarity and spectral asymptotics for the continuum random tree

2008 ◽  
Vol 118 (5) ◽  
pp. 730-754 ◽  
Author(s):  
David Croydon ◽  
Ben Hambly
Keyword(s):  
Spectral Asymptotics ◽  
Random Tree ◽  
Self Similarity ◽  
Continuum Random Tree ◽  
The Continuum

scholarly journals The Continuum Random Tree III

1993 ◽  
Vol 21 (1) ◽  
pp. 248-289 ◽  
Author(s):  
David Aldous
Keyword(s):  
Random Tree ◽  
Continuum Random Tree ◽  
The Continuum

scholarly journals The Continuum Random Tree. I

1991 ◽  
Vol 19 (1) ◽  
pp. 1-28 ◽  
Author(s):  
David Aldous
Keyword(s):  
Random Tree ◽  
Continuum Random Tree ◽  
The Continuum

scholarly journals A Construction of a β-Coalescent via the Pruning of Binary Trees

2013 ◽  
Vol 50 (3) ◽  
pp. 772-790 ◽  
Author(s):  
Romain Abraham ◽  
Jean-François Delmas
Keyword(s):  
State Space ◽  
Binary Tree ◽  
Time Change ◽  
Random Tree ◽  
Binary Trees ◽  
Continuum Random Tree ◽  
Coalescent Process ◽  
Continuous State Space ◽  
Continuous State ◽  
Continuous Analogue

Considering a random binary tree with n labelled leaves, we use a pruning procedure on this tree in order to construct a β(3/2,1/2)-coalescent process. We also use the continuous analogue of this construction, i.e. a pruning procedure on Aldous's continuum random tree, to construct a continuous state space process that has the same structure as the β-coalescent process up to some time change. These two constructions enable us to obtain results on the coalescent process, such as the asymptotics on the number of coalescent events or the law of the blocks involved in the last coalescent event.

scholarly journals A Construction of a β-Coalescent via the Pruning of Binary Trees

2013 ◽  
Vol 50 (03) ◽  
pp. 772-790 ◽  
Author(s):  
Romain Abraham ◽  
Jean-François Delmas
Keyword(s):  
State Space ◽  
Binary Tree ◽  
Time Change ◽  
Random Tree ◽  
Binary Trees ◽  
Continuum Random Tree ◽  
Coalescent Process ◽  
Continuous State Space ◽  
Continuous State ◽  
Continuous Analogue

Considering a random binary tree withnlabelled leaves, we use a pruning procedure on this tree in order to construct a β(3/2,1/2)-coalescent process. We also use the continuous analogue of this construction, i.e. a pruning procedure on Aldous's continuum random tree, to construct a continuous state space process that has the same structure as the β-coalescent process up to some time change. These two constructions enable us to obtain results on the coalescent process, such as the asymptotics on the number of coalescent events or the law of the blocks involved in the last coalescent event.

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