Probabilistic Cellular Automata by Pierre-Yves Louis & Francesca R. Nardi

Probabilistic Cellular Automata by Pierre-Yves Louis & Francesca R. Nardi

Author:Pierre-Yves Louis & Francesca R. Nardi
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham


This result was further improved by [4] into an almost-sure convergence (Fig. 12.4).

Fig. 12.4What Theorem 3 says, for large t

12.3.1 The Link with First-Passage Percolation

The Eden model is a dynamical model of growth process but in fact it can be seen as a static model. To do so, set as before, for ,

As in the previous section, if and only if there is a path of neighbouring cells going from to

such that successive updating along turn into . Then one can show that, for each fixed ,



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