1. The threshold regime of finite volume bootstrap percolation
- Author
-
Raphaël Cerf and Francesco Manzo
- Subjects
Statistics and Probability ,Pure mathematics ,Bootstrap percolation ,Finite volume method ,Applied Mathematics ,Existence theorem ,Monotonic function ,Exponential function ,Combinatorics ,Iterated function ,Modelling and Simulation ,Modeling and Simulation ,Bounded function ,Percolation ,Mathematics - Abstract
We prove that the threshold regime for bootstrap percolation in a d -dimensional box of diameter L with parameters p and l, where 3⩽l⩽ d , is L∼ exp ° (l−1) (Cp −1/(d−l+1) ) , where exp° (l−1) is the exponential iterated l−1 times and C is bounded from above and from below by two positive constants depending on d , l only.
- Published
- 2002
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