The discrete version of the famous Bak-Sneppen model (https://en.wikipedia.org/wiki/Bak-Sneppen_model) is a Markov chain on the space of {0,1} sequences of length n with periodic boundary conditions, which runs as follows. Fix some 0

Barbay and Kenyon (2001) claimed that the fraction of zeros in the stationary distribution becomes negligible when n goes to infinity whenever p>0.54. This result is indeed correct, however, its proof is not.

I shall present the rigorous proof of the Barbay and Kenyon's result, as well as some better bounds for the critical p.

Rigorous bounds for the discrete Bak-Sneppen model