How to cite item

On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees

   
@article{EJP2822,
	author = {Jean Bertoin},
	title = {On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {Random  recursive tree,  giant cluster, fluctuations, super-critical percolation.},
	abstract = {We consider a Bernoulli bond percolation on a random recursive tree of size $n\gg 1$, with supercritical parameter $p_n=1-c/\ln n$ for some $c>0$ fixed. It is known that with high probability, there exists then a unique giant cluster of size $G_n\sim e^{-c}n$, and it follows from a recent result of Schweinsberg that $G_n$ has non-Gaussian fluctuations. We provide an  explanation of this  by analyzing the effect of percolation on different phases of the growth of recursive trees.  This alternative approach may be useful for studying percolation on other classes of trees, such as for instance regular trees.

},
	pages = {no. 24, 1-15},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-2822},    
        url = {http://ejp.ejpecp.org/article/view/2822}}