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Poisson point process limits in size-biased Galton-Watson trees

   
@article{EJP73,
	author = {Jochen Geiger},
	title = {Poisson point process limits in size-biased Galton-Watson trees},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {5},
	year = {2000},
	keywords = {Galton-Watson process, random tree,  point process, limit laws},
	abstract = {Consider a critical binary continuous-time Galton-Watson tree  size-biased according to the number of particles at time $t$.   Decompose the population at $t$ according to the particles'  degree of relationship with a distinguished  particle picked purely at random from those alive  at $t$.  Keeping track of the times when the different families   grow out  of the distinguished line of descent and the related family sizes at $t$,  we represent this relationship structure as a point process  in a time-size plane. We study limits of  these point processes  in the single- and  some multitype case.},
	pages = {no. 17, 1-12},
	issn = {1083-6489},
	doi = {10.1214/EJP.v5-73},    
        url = {http://ejp.ejpecp.org/article/view/73}}