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math.PR2013★ 3 cited
The gaps between the sizes of large clusters in 2D critical percolation
Jacob van den Berg, Rene Conijn
Consider critical bond percolation on a large 2n by 2n box on the square lattice. It is well-known that the size (i.e. number of vertices) of the largest open cluster is, with high…
math.PR2013★ 5 cited
Sharpness versus robustness of the percolation transition in 2D contact processes
J. van den Berg, J. E. Björnberg, M. Heydenreich
We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [1…