Bootstrap percolation and percolation

[MiKiDe]

I read about bootstrap percolation and I would like to find links and similarities between bootstrap percolation and percolation (the initial model).
I wonder if there is any result in percolation that is still valid in the bootstrap model.

 

[mmwave]

Hello,

Thank you for your interest in bootstrap percolation and its relationship to the initial percolation model. Bootstrap percolation is a variation of the percolation model that was introduced by mathematician Joel Spencer in 1979. It has since been studied extensively and has been applied to various fields such as physics, biology, and computer science.

Percolation, on the other hand, is a well-known mathematical model that was first introduced by Broadbent and Hammersley in 1957. It has been extensively studied and has numerous applications in various fields such as physics, chemistry, and sociology.

There are indeed links and similarities between bootstrap percolation and percolation. In fact, bootstrap percolation can be seen as an extension of the initial percolation model. Both models involve the concept of occupying or activating nodes in a network, and both have a critical threshold at which a giant component emerges.

One of the main differences between the two models is the mechanism of activation. In the initial percolation model, nodes are activated randomly, while in bootstrap percolation, nodes are activated based on a predetermined rule. However, there are results in percolation that are still valid in the bootstrap model.

For example, the critical threshold for the emergence of a giant component in bootstrap percolation is the same as in the initial percolation model. This result was first proven by Spencer in 1979 and has since been extended and generalized by other researchers.

Additionally, the concept of self-organized criticality, which is a key aspect of percolation, has also been studied in bootstrap percolation. In particular, it has been shown that bootstrap percolation exhibits self-organized criticality in certain cases.

In conclusion, while bootstrap percolation is a variation of the initial percolation model, there are still many similarities and results that are valid in both models. I hope this helps to answer your question. Please let me know if you have any further inquiries. Thank you.