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Erdos-Renyi random graphs + forest fires = self-organized criticality

   
@article{EJP653,
	author = {Balazs Rath and Balint Toth},
	title = {Erdos-Renyi random graphs + forest fires = self-organized criticality},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {forest fire model, Erdos-Renyi random graph, Smoluchowski coagulation equations, self-organized criticality},
	abstract = {We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent.},
	pages = {no. 45, 1290-1327},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-653},    
        url = {http://ejp.ejpecp.org/article/view/653}}