Critical length for semi-oriented bootstrap percolation

T. S. Mountford

Stochastic Processes and their Applications, 1995, vol. 56, issue 2, 185-205

Abstract: 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.

Keywords: Bootstrap; percolation; Critical; lengths; Exponential; rates (search for similar items in EconPapers)
Date: 1995
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