Critical length for semi-oriented bootstrap percolation

We consider the behaviour of semi-oriented bootstrap percolation restricted to a finite square or torus. We prove that as the probability of initial occupancy p tends to zero, the side length required for a two-dimensional torus to have non-negligible chance of filling itself up is between for universal constants c and C. We show similar results for the side length required for a square to show significant clustering behaviour.

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Year of publication:	1995
Authors:	Mountford, T. S.
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 56.1995, 2, p. 185-205
Publisher:	Elsevier
Keywords:	Bootstrap percolation Critical lengths Exponential rates

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008875781